The goal of this clinical trial is to see the safety and efficacy of pembrolizumab and lenvatinib in patients with anal squamous cell cancer that cannot be removed through surgery or is spread to other organs. Eligible participants should have also received some form of standard therapy previously for their advanced cancer.

Participants will be required to come for a clinic visit and infusion of pembrolizumab. Lenvatinib will be taken by mouth at home based on direction provided by physicians and research team.

After signing this consent, participants will undergo a screening visit that includes a blood draw, physical exam and medical history review. Once screening is complete, and a participant is found to be eligible for the study, they will be required to come for a clinic visit and infusion of pembrolizumab. Lenvatinib will be taken by mouth at home based on direction provided research team. Each visit will take approximately 3hours including clinic visit and infusion visit. Participants will also be asked to complete a diary to ensure they are taking lenvatinib pills as directed by their physician. During clinic visits, participants will be asked about side effects from therapy, any new symptoms, they will be examined and their blood pressure and other tests will be monitored throughout the study. Total study duration for most participants is expected to be approximately 6 months, however, it can be longer or shorter, depending upon whether a participant is benefitting from therapy or not, or if they are having any serious side effects from therapy.

Inclusion Criteria:

1. Male/female participants who are at least 18 years of age on the day of signing informed consent with histologically confirmed diagnosis of anal squamous cell carcinoma.

2. The participants should have inoperable local recurrence or advanced cancer (stage 4; any T, any N, M1).

3. The participants should have received at least one prior line of cytotoxic chemotherapy regimen in palliative setting or have declined cytotoxic chemotherapy use or have a contraindication to receive chemotherapy. Prior use of PD-1 systemic therapy is allowed

4. ECOG Performance status: 0, 1 or 2.

5. Adequate organ and bone marrow function as outlined below:

   • Absolute neutrophil count (ANC): ≥1500/µL
   • Platelets: ≥100 000/µL
   • Creatinine; creatinine clearance GFR can also be used in place of creatinine or CrCl): Creatinine ≤1.5 × ULN OR Creatinine Clearance ≥30 mL/min for participant with creatinine levels >1.5 × institutional ULN
   • Total bilirubin: ≤1.5 ×ULN OR direct bilirubin ≤ULN for participants with total bilirubin levels >1.5 × ULN
   • aspartate aminotransferase (serum glutamic oxaloacetic transaminase) - AST (SGOT) and ALT (SGPT)=alanine aminotransferase (serum glutamic pyruvic transaminase) - ALT (SGPT): ≤2.5 × ULN (≤5 × ULN for participants with liver metastases) International normalized ratio (INR) OR prothrombin time (PT) Activated partial thromboplastin time (aPTT): INR ≤1.5 × ULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants

6. A participant will be eligible for inclusion in the study if the participant:

   Female Participants

   • Is not a Women Of Child Bearing Potential (WOCBP): OR

   • Is a WOCBP and agrees to use a contraceptive method that is highly effective (with a failure rate of <1% per year), with low user dependency, or be abstinent from heterosexual intercourse as their preferred and usual lifestyle (abstinent on a long term and persistent basis), as described in Appendix D during the intervention period and for at least 120 days post pembrolizumab or 30 days post lenvatinib, whichever date occurs last. The investigator should evaluate the potential for contraceptive method failure (i.e., noncompliance, recently initiated) in relationship to the first dose of study intervention.

   • A WOCBP must have a negative highly sensitive pregnancy test (urine or serum as required by local regulations) during screening (for the purpose of confirming eligibility/enrollment).
   • Note: If a urine test cannot be confirmed as negative (e.g., an ambiguous result), a serum pregnancy test is required. In such cases, the participant must be excluded from participation if the serum pregnancy result is positive. (WOCBP should also have a negative pregnancy test within 24 hours before the first dose of study intervention (cycle1 day 1) as described in schedule of Activities Table).

   Male Participants

   Male participants are eligible to participate if they agree to the following during the intervention period and for at least 7 days after the last dose of lenvatinib:

   • Be abstinent from heterosexual intercourse as their preferred and usual lifestyle (abstinent on a long term and persistent basis) and agree to remain abstinent OR

   • Must agree to use contraception unless confirmed to be azoospermic (vasectomized or secondary to medical cause) as detailed below and in Appendix D:

     • Agree to use a male condom plus partner use of an additional contraceptive method when having penile-vaginal intercourse with a WOCBP who is not currently pregnant. Note: Men with a pregnant or breastfeeding partner must agree to remain abstinent from penile-vaginal intercourse or use a male condom during each episode of penile-vaginal penetration.
     • Contraceptive use by men should be consistent with local regulations regarding the methods of contraception for those participating in clinical studies. If the contraception requirements in the local label for any of the study interventions is more stringent than the requirements above, the local label requirements are to be followed.

   • Please note that 7 days after lenvatinib is stopped, if the participant is on pembrolizumab only, no male contraception measures are needed.

7. Have measurable disease based on RECIST 1.1. Lesions situated in a previously irradiated area are considered measurable if progression has been demonstrated in such lesions.

8. Archival tumor tissue sample or fresh core biopsy of a tumor lesion is available. In a situation where a safe and suitable site for a fresh biopsy is not feasible and an archival tissue is not available; patients may still be eligible to enroll after discussing with UTSW PI.

9. Have adequately controlled BP with or without antihypertensive medications, defined as BP ≤150/90 mm Hg with no change in antihypertensive medications within 1 week before C1D1.

10. The subject's urinary protein is < 1+ on dipstick or routine urinalysis; if urine protein > 2+, a 24-hour urine must be collected and must demonstrate < 1000 mg of protein in 24 hours to allow participation in the study.

11. Has a left ventricle ejection fraction > 45% as determined by multi-gated acquisition (MUGA) or 2D echocardiogram (ECHO). If patient is asymptomatic and there is a documented MUGA or 2D ECHO completed in the last 18 months, then this will be adequate to confirm eligibility.

12. Patients receiving therapeutic anticoagulation should be on a stable anticoagulant regimen within 14 days prior to first dose of study drug.

13. Subjects must have recovered from prior treatment-related toxicities to grade 1 or baseline (Some exception to criterion are, alopecia or clinically stable chronic toxicities that may be requiring ongoing medical management but are not affecting daily function as per investigator assessment, e.g. hypothyroidism or chemotherapy-induced neuropathy etc.).

14. Participants who have known history of HBV infection are eligible if they have received HBV antiviral therapy for at least 4 weeks and have undetectable HBV viral load prior to C1D1.

    • Participants should remain on anti-viral therapy throughout study intervention and follow local guidelines for HBV anti-viral therapy post completion of study intervention.

    • Hepatitis B screening tests are not required unless:

      • Known history of HBV infection
      • As mandated by local health authority or institution

15. Participants with known history of HCV infection are eligible if HCV viral load is undetectable at screening.

    • Participants must have completed curative anti-viral therapy at least 4 weeks prior to randomization.

    • Hepatitis C screening tests are not required unless:

      • Known history of HCV infection
      • As mandated by local health authority or institution

16. Participants with known history of HIV infection must have well-controlled HIV on anti-retroviral therapy (ART), defined as:

    • Participants on ART must have a CD4+ T-cell count ≥350 cells/mm3 at the time of screening.
    • Participants on ART must have achieved and maintained virologic suppression defined as confirmed HIV RNA level below 50 or the LLOQ (below the limit of detection) using the locally available assay at the time of screening and for at least 12 weeks before screening.
    • It is advised that participants must not have had any AIDS-defining opportunistic infections within the past 12 months.
    • Participants on ART must have been on a stable regimen, without changes in drugs or dose modification, for at least 4 weeks before study entry (Day 1) and agree to continue ART throughout the study.
    • The combination ART regimen must not contain any antiretroviral medications that interact with CYP3A4 inhibitors/inducers/substrates (https://www.fda.gov/drugs/drug-interactions-labeling/drug-development-and-drug-interactions-table-substrates-inhibitors-and-inducers)

17. Ability to understand and the willingness to sign a written informed consent.

Exclusion Criteria:

1. Has received chemotherapy within 2 weeks prior to starting study treatment.

2. Has received any investigational agents for the treatment of the cancer under study within 3 weeks of start of the study.

3. Has received prior radiotherapy within 3 weeks of start of study intervention or suffers from radiation-related toxicities requiring corticosteroids.

4. Had a major surgery within 3 weeks prior to first dose of study interventions or has not adequately recovered from a previous major surgery or has ongoing surgical complications, in the opinion of the investigator, that would limit participation in study. Note: Adequate wound healing after major surgery must be assessed clinically by investigator or qualified designee.

5. Has an uncontrolled intercurrent illness including, but not limited to, ongoing or active bacterial infection requiring systemic antibiotic, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that, in the opinion of the investigator, would limit compliance with study requirements.

6. Has known active CNS metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided participants are not on steroid treatment for the CNS metastasis at least 14 days prior to first dose of study intervention. An MRI assessment of the brain may be needed during Screening if clinically indicated as per investigator.

7. Has preexisting ≥Grade 3 gastrointestinal or non-gastrointestinal fistula

8. Has a left ventricle ejection fraction <45% as determined by multi-gated acquisition (MUGA) or 2D echocardiogram (ECHO). Among patients with a prior known history of congestive heart failure with a low ejection fraction, then ejection fraction assessment will be performed during screening to determine eligibility.

9. Has clinically significant cardiovascular disease within 12 months from first dose of study intervention, including New York Heart Association Class III or IV congestive heart failure, unstable angina, myocardial infarction, cerebral vascular accident, or cardiac arrhythmia associated with hemodynamic instability. Note: Medically controlled arrhythmia would be permitted.

10. Has radiographic evidence of encasement or invasion of a major blood vessel, or of intratumoral cavitation. NOTE: The degree of proximity to major blood vessels should be considered because of the potential risk of severe hemorrhage associated with tumor shrinkage/necrosis following lenvatinib therapy.

11. Have prolongation of QTc interval to >480 ms.

12. Has a history of gastrointestinal malabsorption or any other condition that might affect the absorption of lenvatinib in the opinion of the investigator.

13. Has an active hemoptysis (bright red blood of at least 0.5 teaspoon) within 3 weeks prior to the first dose of study drug.

14. Has received a live vaccine or live-attenuated vaccine within 30 days before the first dose of study intervention. Administration of killed vaccines is allowed.

15. Has received chronic systemic steroid therapy (exceeding 10 mg daily dose of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to the first dose of study drug.

16. Has active autoimmune disease that has required systemic treatment in the past 2 years except replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid).

17. Has a known additional malignancy that is progressing or has required active systemic treatment within the past 2 years. Note: Participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin or carcinoma in situ (excluding carcinoma in situ of the bladder) that have undergone potentially curative therapy are not excluded. Participants with low-risk early-stage prostate cancer (T1-T2a, Gleason score ≤6, and PSA <10 ng/mL) either treated with definitive intent or untreated in active surveillance with stable disease are not excluded.

18. Has severe hypersensitivity (≥Grade 3) to pembrolizumab and/or any of its excipients.

19. History of allergic reactions attributed to compounds of similar chemical or biologic composition to Lenvatinib or Pembrolizumab used in study.

20. Has a history of (non-infectious) pneumonitis/interstitial lung disease that required steroids or has current pneumonitis/interstitial lung disease.

21. Has a concurrent active Hepatitis B (defined as HBsAg positive and/or detectable HBV DNA) and Hepatitis C virus (defined as anti-HCV Ab positive and detectable HCV RNA) infection.

    Note: Hepatitis B and C screening tests are not required unless:

    • Known history of HBV and HCV infection
    • As mandated by local health authority or institution

22. Has had an allogenic tissue/solid organ transplant.