To evaluate the increase in Overall Response Rate (ORR) in the pembrolizumab alone arm compared to the pembrolizumab after SBRT arm at 12 weeks

The investigators hypothesize that in a significant subset of patients with recurrent NSCLC immunotherapy after SBRT will be superior to treatment with immunotherapy alone and that SBRT, given to a single metastatic site of the tumor, will augment the immune response to the tumor. Objectives: Disease Control Rate (DCR), defined as the percentage of patients having a complete response, partial response or stable disease at 12 weeks, PFS, defined as time from randomization to disease progression or death, OS, defined as time from randomization to death (of any cause). Toxicity.

Inclusion Criteria:

1. Be willing and able to provide written informed consent/assent for the trial.

2. Be ≥ 18 years of age on day of signing informed consent.

3. Have measurable disease based on RECIST 1.1.

4. Must provide newly obtained tissue from a core or excisional biopsy of a tumor lesion and are willing to have a second biopsy performed form any non-irradiated lesion after the radiation and immune-modulating treatment.

5. Have a performance status of 0 or 1 on the ECOG Performance Scale.

6. Stage IV NSCLC; treated with at least 1 regimen of chemotherapy.

7. Have at least 2 separate (metastatic) lesions of which one is amenable for irradiation with a size of < 5 cm.

8. Demonstrate adequate organ function:

   Absolute neutrophil count (ANC) ≥1,500 /mcL; Platelets ≥100,000 / mcL; Hemoglobin ≥9 g/dL or ≥5.6 mmol/L; Serum creatinine ≤1.5 X upper limit of normal (ULN) OR measured or calculated creatinine clearance (GFR can also be used in place of creatinine or CrCl) ≥50 mL/min for subject with creatinine levels > 1.5 X institutional ULN; Serum total bilirubin ≤ 1.5 X ULN OR Direct bilirubin ≤ ULN for subjects with total bilirubin levels > 1.5 ULN; AST (SGOT) and ALT (SGPT) ≤ 2.5 X ULN OR ≤ 5 X ULN for subjects with liver metastases; International Normalized Ratio (INR) or Prothrombin Time (PT) and Activated Partial Thromboplastin Time (aPTT) ≤1.5 X ULN unless subject is receiving anticoagulant therapy as long as PT or PTT is within therapeutic range of intended use of anticoagulants.

   All screening labs should be performed within 10 days of treatment initiation.

9. Female subject of childbearing potential should have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required.

10. Female subjects of childbearing potential should be willing to use 2 methods of birth control or be surgically sterile, or abstain from heterosexual activity for the course of the study through 120 days after the last dose of study medication (Reference Section 5.7.2). Subjects of childbearing potential are those who have not been surgically sterilized or have not been free from menses for > 1 year.

11. Male subjects should agree to use an adequate method of contraception starting with the first dose of study therapy through 120 days after the last dose of study therapy.

Exclusion Criteria:

1. Is currently participating in or has participated in a study of an investigational agent or using an investigational device within 4 weeks of the first dose of treatment.

2. Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment.

3. Has had a prior monoclonal antibody within 4 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier.

4. Has had prior chemotherapy or targeted small molecule therapy within 4 weeks prior to study Day 1 or who has not recovered (i.e., ≤ Grade 1 or at baseline) from adverse events due to a previously administered agent.

   • Note: Subjects with ≤ Grade 2 neuropathy are an exception to this criterion and may qualify for the study.
   • Note: If subjects received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention prior to starting therapy.

5. Have had previous radical radiation to any tumor site within 6 months prior to study Day 1.

6. Have known but untreated driver mutations of the EGFR gene or ALK translocation.

7. Has a known additional malignancy that is progressing or requires active treatment. Exceptions include basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or in situ cervical cancer that has undergone potentially curative therapy. 8. Has known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Subjects with previously treated brain metastases may participate provided they are stable (without evidence of progression by imaging for at least six weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 14 days prior to trial treatment.

9. Has an active autoimmune disease requiring systemic treatment within the past 3 months or a documented history of clinically severe autoimmune disease, or a syndrome that requires systemic steroids or immunosuppressive agents. Subjects with vitiligo or resolved childhood asthma/atopy would be an exception to this rule. Subjects that require intermittent use of bronchodilators or local steroid injections would not be excluded from the study. Subjects with hypothyroidism stable on hormone replacement or Sjögren's syndrome will not be excluded from the study.

10. Has evidence of symptomatic interstitial lung disease or an active, non-infectious pneumonitis.

11. Has an active infection requiring systemic therapy. 12. Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not in the best interest of the subject to participate, in the opinion of the treating investigator.

13. Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial.

14. Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment.

15. Has received prior therapy with an anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CD137, or anti-Cytotoxic T-lymphocyte-associated antigen-4 (CTLA-4) antibody (including ipilimumab or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways).

16. Has a known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies).

17. Has known active Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (e.g., HCV RNA [qualitative] is detected).

18. Has received a live vaccine within 30 days prior to the first dose of trial treatment.

19. Has had major surgery or major blood transfusions (>3 packed cells) in the past 3 months.