The purpose of this research study is to see if loncastuximab tesirine has any benefits at dose levels researchers found acceptable in earlier studies in patients with related forms of immune cell cancers. The researchers want to find out the effects (good and bad) that loncastuximab tesirine has on the participant and the participant's condition.

Inclusion Criteria:

1. Men and women, aged 18 years or older.

2. Histologically confirmed MZL, including extranodal, nodal, and splenic subtypes.

3. Previously received 1 or more lines of systemic therapy, including at least 1 anti-CD20 antibody (cluster of differentiation antigen 20) (either as monotherapy or in combination as chemoimmunotherapy), with documented progression or documented failure to achieve CR or PR after the most recent systemic treatment regimen. Subjects with H. pylori-positive gastric extranodal MZL who received an initial treatment with currently accepted antibiotics may be considered eligible if, after antibiotic regimen, subject has histologically confirmed MZL and was subsequently treated with at least 1 line of systemic therapy.

4. Radiographically measurable lymphadenopathy or extranodal lymphoid malignancy (defined as the presence of ≥ 1 lesion that measures > 1.5 cm in the LDi and ≥ 1.0 cm in the longest perpendicular diameter as assessed by CT or MRI per response criteria for lymphomas.68 Imaging must be conducted within 6 weeks prior to the start of therapy.

   1. Subjects with splenic MZL who do not meet the radiographically measurable disease criteria described herein are eligible for participation provided that bone marrow infiltration of MZL is histologically confirmed.
   2. Subjects with skin EMZL (extranodal marginal zone lymphoma) who do not meet the radiographically measurable disease criteria described herein are eligible for participation provided that skin lesion measures ≥ 1.5 cm in diameter by tape measure and is documented by photo or there are multiple skin lesions measuring >1cm in diameter on the body that cannot be incorporated in one radiation field and at least one of them is histologically confirmed as MZL.
   3. Subjects with gastric extranodal MZL histologically confirmed and need therapy but do not have measurable disease and in which response to treatment can be assess by multiple random gastric biopsies.
   4. Subjects with conjunctival EMZL who do not meet the radiographically measurable disease criteria described herein are eligible for participation provided that conjunctival lesion measures ≥ 1 cm in diameter by tape measure and is documented by photo or there are multiple conjunctival lesions measuring together >1 5cm that cannot be treated by radiation because of previous radiation therapy, contraindications to radiation and patient refusal to receive radiation therapy. At least one of these lesions needs be histologically confirmed as MZL.

5. Subjects must be willing to provide a lymph node or tissue biopsy from the most recent available archival tissue or undergo an incisional or excisional lymph node or tissue biopsy.

   a. Subjects with splenic MZL who do not have a tumor to biopsy or an archival tumor tissue sample are eligible for participation provided subject is willing to undergo a bone marrow biopsy or provide an archival bone marrow biopsy that was obtained before the date of the first dose of study treatment; bone marrow sample must show histologically confirmed infiltration of MZL.

6. Patient should have at least one of the following criteria for treatment initiation):

   • Involvement of ≥3 nodal sites, each with diameter of ≥3 cm
   • Any nodal or extranodal tumor mass with a diameter of ≥5 cm
   • B symptoms (fever ≥ 38 degrees Celsius of unclear etiology, night sweats, weight loss > 10% within the prior 6 months) or other symptoms attributed to disease or specific organ involvement associated with the relapse.
   • Risk of local compressive symptoms that may result in organ compromise
   • Splenomegaly or splenic lesion without splenomegaly
   • Leukopenia attributed to MZL (leukocytes < 1000/mm3)
   • Leukemia (> 5.000 lymphoma cells/mm3)
   • Threatened organ function, especially for extranodal MZL
   • Requirement for transfusion or growth factor support attributed to lymphoma
   • Involvement of 2 or more extranodal sites, with tumor/lesion in each extranodal site ≥1 cm
   • Progression or relapsed within 24 months after MZL diagnosis in patients previously treated with ≥1 line of systemic therapy

7. Life expectancy > 3 months.

8. ECOG (Eastern Cooperative Oncology Group ) performance status 0 to 2 (Refer to Appendix A).69

9. Adequate hematologic, hepatic, and renal function tested within 6 weeks prior to the start of therapy (values must not be achieved with growth factors):

   1. ANC (absolute neutrophil count ) ≥ 1.0 × 109/L.
   2. Hemoglobin ≥ 8.0 g/dL.
   3. Platelet count ≥ 50 × 109/L.
   4. Total bilirubin ≤ 1.5 × ULN (upper limit of normal ). Subjects with documented history of Gilbert's syndrome and in whom total bilirubin elevations are accompanied by elevated indirect bilirubin are eligible.
   5. ALT(alanine aminotransferase) /AST (aspartate aminotransferase ) ≤ 3.0 ULN or ≤ 5 × ULN in the presence of liver involvement by lymphoma.
   6. Calculated creatinine clearance ≥ 45 mL/min by the Cockcroft-Gault Equation70 or the estimated glomerular filtration rate ≥ 45 mL/min/1.73 m2 using the Modification of Diet in Renal Disease formula.

10. Willingness to avoid pregnancy or fathering children based on the criteria below:

    1. Woman of nonchildbearing potential (ie, surgically sterile with a hysterectomy and/or bilateral oophorectomy OR ≥ 12 months of amenorrhea and at least 45 years of age).
    2. Woman of childbearing potential who has a negative serum pregnancy test at screening and who agrees to take appropriate precautions to avoid pregnancy (with at least 99% certainty) from screening through safety follow-up at least 9 months after the last dose of loncastuximab tesirine. Permitted methods that are at least 99% effective in preventing pregnancy should be communicated to the subject and their understanding confirmed.

11. Man, who agrees to take appropriate precautions to avoid fathering children (with at least 99% certainty) from screening through at least 6 months after the last dose of study treatment. Permitted methods that are at least 99% effective in preventing pregnancy should be communicated to the subject and their understanding confirmed.

Exclusion Criteria:

1. Evidence of DLBCL transformation. a. Subjects with presumptive evidence of transformation based on clinical assessment of factors such as, but not limited to, increasing lactate dehydrogenase, rapidly worsening disease, or frequent B-symptoms, must be ruled out for a transformation to a more aggressive disease, such as DLBCL.

2. History of central nervous system lymphoma (either primary or metastatic) or leptomeningeal disease.

3. Concurrent anticancer therapy (eg, chemotherapy, radiation therapy, surgery, immunotherapy, biologic therapy, hormonal therapy, investigational therapy, or tumor embolization).

4. Allogeneic stem cell transplant within the last 6 months, or autologous stem cell transplant within the last 3 months before the date of the first dose of study treatment.

5. Active graft versus host disease.

6. Receipt of anticancer medications or investigational drugs within the following intervals before the date of the first dose of study treatment:

   1. < 10 weeks from completion of any radio- or toxin-immunoconjugates.
   2. < 4 weeks for immunotherapy
   3. <. 3 weeks for radiotherapy.
   4. < 2 weeks for any investigational agent or other anticancer medications.
   5. Steroids that are used for treatment of allergy or other underlying condition are permittable, but not steroids started to treat lymphoma. Subjects receiving corticosteroids must be at a dose level ≤ 10 mg/day within 7 days of the study treatment administration.

7. Inadequate recovery from toxicity and/or complications from a major surgery before starting therapy.

8. Prior treatment-related toxicities have not resolved to NCI CTCAE v5.071 ≤ Grade 1 before the date of the first dose of study treatment, except for stable chronic toxicities (≤ Grade 2) not expected to resolve (eg, stable Grade 2 peripheral neurotoxicity).

9. Previous treatment with anti CD19 (cluster of differentiation antigen 19 ) approaches

10. Current or previous other malignancy within 3 years of study entry, except cured basal or squamous cell skin cancer, superficial bladder cancer, prostate intraepithelial neoplasm, carcinoma in situ of the cervix, or other noninvasive or indolent malignancy.

11. Significant concurrent, uncontrolled medical condition, including, but not limited to, renal, hepatic, hematological, GI, endocrine, pulmonary, neurological, cerebral, or psychiatric disease. Patients with pleural effusion, pericardial effusion or ascites should not be enrolled in this study, unless effusions are caused by lymphoma.

12. Chronic or current active infectious disease requiring systemic antibiotics, antifungal, or antiviral treatment or exposure to a live vaccine within 30 days of dosing.

13. Known HIV infection or positivity on immunoassay. Note: HIV screening test is optional

14. Liver disease: HBV (hepatitis B virus) or HCV (hepatitis C virus) infection: Subjects positive for HBsAg or hepatitis B core antibody will be eligible if they are negative for HBV-DNA; these subjects should be considered for prophylactic antiviral therapy. Subjects positive for anti-HCV antibody will be eligible if they are negative for HCV-RNA.

15. Current New York Heart Association Class II to IV congestive heart failure or uncontrolled arrhythmia.

16. Uncontrolled or symptomatic arrhythmia, stroke in last 6 months, liver cirrhosis, and autoimmune disorder requiring immunosuppression or long-term corticosteroids (>10 mg daily prednisone equivalent)

17. Currently pregnant or breastfeeding.

18. Any condition that would, in the investigator's judgment, interfere with full participation in the study, including administration of study treatment and attending required study visits; pose a significant risk to the subject; or interfere with interpretation of study data.

19. Patients with impaired decision-making capacity