Phase II Study of Peptide Receptor Radionuclide Therapy in Combination With Immunotherapy for Patients With Merkel Cell Cancer

Inclusion Criteria: 1. Written informed consent and HIPAA authorization for release of personal health information prior to registration. NOTE: HIPAA authorization may be included in the informed consent or obtained separately. 2. Male and female, age ≥ 18 years at the time of consent. 3. ECOG Performance Status of 0-1 within 28 days prior to registration. 4. Histological or cytological evidence of Merkel cell cancer per AJCC, 8th edition. 5. Presence of somatostatin receptors by Ga-68 dotatate (or equivalent) imaging, which is a requirement for PRRT (lutetium Lu 177 dotatate \[Lutathera®\]). Must have at least one measurable lesion per RECIST 1.1. 6. Must have progressed on treatment with an anti-PD-1/L1 mAb administered either as monotherapy or in combination with other checkpoint inhibitors or other therapies. PD-1 treatment progression is defined by meeting all of the following criteria: * Has received at least 2 doses of an approved anti-PD-1/L1 mAb * Has demonstrated disease progression after anti-PD-1/L1 as defined by RECIST v1.1. * Progressive disease has been documented within 12 weeks from the last dose of anti-PD-1/L1 mAb. Note: This determination is made by the local investigator. Once disease progression is confirmed, the initial date of disease progression documentation will be considered the date of disease progression. 7. Prior cancer treatment must be completed and the subject must have recovered from all reversible acute toxic effects of the regimen (other than alopecia) to Grade ≤ 1 or baseline. 8. Demonstrate adequate organ function as defined in the table below. All screening labs to be obtained within 28 days prior to registration. * Hematological: * Absolute Neutrophil Count (ANC): ≥ 1500/uL * Platelets: ≥100,000/uL * Hemoglobin (Hgb): ≥9.0g/dL or ≥5.6mmol/L * Renal: * Creatinine: 1.5 x ULN OR * Measured or calculated creatinine clearance (GFR can also be used in place of creatinine or CrCl): ≥30mL/min for participant with creatinine levels \>1.5 x institutional ULN * Hepatic: ---Total bilirubin: ≤1.5 x ULN OR direct bilirubin ≤ULN for participants with total bilirubin levels \>1.5 x ULN * AST(SGOT) and ALT(SGPT): ≤2.5 x ULN (≤5 x ULN for participants with liver metastases) * Coagulation: * International normalized ratio (INR) OR prothrombin time (PT): ≤1.5 × ULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants * Activated partial thromboplastin time (aPTT): ≤1.5 × ULN unless participant is receiving anticoagulant therapy as long as PT or aPTT is within therapeutic range of intended use of anticoagulants 9. Females of childbearing potential who are sexually active with a male able to father a child must have a negative serum pregnancy test within 7 days prior to registration. 10. Females of childbearing potential who are sexually active with a male able to father a child must be willing to abstain from heterosexual activity or to use an effective method(s) of contraception from the time of informed consent, during the study and for 7 months after the last dose of study drug(s). Males able to father a child who are sexually active with female of childbearing potential must be willing to abstain from heterosexual activity or to use an effective method(s) of contraception from initiation of treatment, during the study and for 120 days after the last dose of study drug(s). 11. Participants who are HBsAg positive are eligible if they have received HBV anti-viral therapy for at least 4 weeks and have undetectable HBV viral load prior to registration. Note: 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 12. Participants with a history of HCV infection are eligible if HCV viral load is undetectable at screening. Note: 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 13. HIV-infected participants must have well-controlled HIV on anti-retroviral therapy (ART), defined as: 1. Participants on ART must have a CD4+ T-cell count ≥350 cells/mm3 at the time of screening 2. 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 3. It is advised that participants must not have had any AIDS-defining opportunistic infections within the past 12 months. 4. 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 NOTE: HIV-infected participants with a history of Kaposi's sarcoma and/or Multicentric Castleman's Disease are excluded. 14. As determined by the enrolling physician or protocol designee, ability of the subject to understand and comply with study procedures for the entire length of the study. Exclusion Criteria Subjects meeting any of the criteria below may not participate in the study: 1. Has known additional malignancy that is progressing or has required active treatment within the past 3 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. Patients with controlled CLL must be off all therapy for at least 6 months. 2. Has known active CNS metastases and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are radiologically stable, i.e. without evidence of progression for at least 4 weeks by repeat imaging (note that the repeat imaging should be performed during study screening), clinically stable and without requirement of steroid treatment for at least 14 days prior to first dose of study intervention. 3. Has received a live vaccine or live-attenuated vaccine within 30 days prior to the first dose of study drug. Administration of killed vaccines is allowed. 4. Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to registration. 5. Has had an allogeneic tissue/solid organ transplant. 6. Has severe hypersensitivity (≥Grade 3) to pembrolizumab and/or any of its excipients. 7. Has active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment. 8. Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis. 9. Has an active infection requiring systemic therapy. 10. Has active TB (Bacillus Tuberculosis) infection. 11. Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the subject's participation for the full duration of the study, or is not in the best interest of the subject to participate, in the opinion of the treating investigator. 12. Has known psychiatric or substance abuse disorders that would interfere with cooperation with the requirements of the trial. 13. Is pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the study, starting with the screening visit through 7 months (females) or 120 days (males) after the last dose of trial treatment. NOTE: breast milk cannot be stored for future use while the mother is being treated on study. 14. Clinically significant cardiovascular disease or cardiac insufficiency (New York Heart Association classes III-IV), cardiomyopathy, preexisting clinically significant arrhythmia, acute myocardial infarction within 3 months of enrollment, angina pectoris within 3 months of enrollment.