177Lu-PSMA-617 and Pembrolizumab in Treating Patients With Metastatic Castration-Resistant Prostate Cancer

Inclusion Criteria:

• The subject is able and willing to comply with study procedures and provide signedand dated informed consent

• Histologically confirmed prostate adenocarcinoma. De novo small cell neuroendocrineprostate cancer will not be allowed due to putative lower PSMA expression in thistumor subtype. Treatment-emergent small cell neuroendocrine prostate cancer detectedin metastatic tumor biopsy is not an exclusion

• A minimum of three PSMA-avid lesions on baseline 68Ga-PSMA-11 PET, with positivelesions defined as those with maximum standardized uptake value (SUVmax) valuesgreater than liver.

• Progressive metastatic castration-resistant prostate cancer by Prostate CancerWorking Group (PCWG)3 criteria at the time of study entry

• Castrate level of serum testosterone at study entry (< 50 ng/dL). Participantswithout prior bilateral orchiectomy are required to remain on luteinizinghormone-releasing hormone (LHRH) analogue treatment for duration of study

• Prior progression on at least one second generation androgen signaling inhibitorincluding abiraterone, apalutamide, darolutamide, and/or enzalutamide

• Absolute neutrophil count > 1.5 x 10^9/L

• Hemoglobin > 9.0 g/dL

• Platelet count > 100,000/microliter

• Serum creatinine =< 1.5 x upper limit of normal (ULN) or estimated glomerularfiltration rate (GFR) > 50 ml/min by Cockcroft-Gault or 24 hour urine collection

• Total bilirubin =< 1.5 x ULN. In participants with known or suspected Gilbert'sdisease, direct bilirubin =< ULN

• Aspartate aminotransferase and alanine aminotransferase =< 2.5 x ULN (<= 5 x ULN inparticipants with liver metastases)

• No other systemic anti-cancer therapies administered other than LHRH analogue within 14 days, or 5 half-lives, whichever is shorter, prior to initiation of studytreatment. Adverse events related to prior anti-cancer treatment other than LHRHanalog treatment must have recovered to Grade <= 1 with the exception of any gradealopecia and grade <= 2 neuropathy.

• Participants must have an Eastern Cooperative Oncology Group (ECOG) performancestatus of 0 or 1

• Participants must use appropriate methods of contraception during study treatmentand for at least 60 days after last study treatment

• Participants who are sexually active should consider their female partner to beof childbearing potential if she has experienced menarche and is notpostmenopausal (defined as amenorrhea > 24 consecutive months) or has notundergone successful surgical sterilization. Even women who use contraceptivehormones (oral, implanted, or injected), an intrauterine device, or barriermethods (diaphragms, condoms, spermicide) should be considered to be ofchildbearing potential

• Participants who have undergone vasectomy themselves should also be consideredto be of childbearing potential

• Acceptable methods of contraception include continuous total abstinence, ordouble-barrier method of birth control (e.g. condoms used with spermicide, orcondoms used with oral contraceptives). Periodic abstinence and withdrawal arenot acceptable methods of contraception

• Participants must provide consent to comply to recommended radioprotectionprecautions during study

• Participants willing to undergo tumor biopsy and have at least one lesion safelyaccessible to tumor biopsy. Bone or soft tissue lesion is allowed

• Measurable disease by RECIST 1.1 criteria

Exclusion Criteria:

• Untreated brain metastases at study entry. Participants with previously treatedbrain metastases are eligible provided the following criteria are all met:

• Last treatment was > 28 days prior to cycle 1 day 1 (C1D1)

• No evidence of new/progressive brain metastases is observed on magneticresonance imaging (MRI) obtained during screening window

• Patient is clinically stable without requirement of steroid treatment for atleast 14 days prior to first dose of study treatment

• Receipt of prior PSMA-directed treatment (e.g. radiotherapy, immunotherapy, orantibody-drug conjugate)

• Prior enrollment on clinical study investigating Lu-PSMA-based radioligand therapy

• Prior treatment with radium-223 or other radioisotope for the treatment of prostatecancer

• Has received prior radiotherapy within 2 weeks of start of study treatment.Participants must have recovered from all radiation-related toxicities, not requirecorticosteroids, and not have had radiation pneumonitis. A 1-week washout ispermitted for palliative radiation (=< 2 weeks of radiotherapy) to non-centralnervous system (CNS) disease

• Receipt of prior pembrolizumab or another immune checkpoint inhibitor (e.g.nivolumab, ipilimumab)

• Is currently participating in or has participated in a study of an investigationalagent or has used an investigational device within 4 weeks prior to the first doseof study treatment

• Note: Participants who have entered the follow-up phase of an investigationalstudy may participate as long as it has been 4 weeks after the last dose of theprevious investigational agent

• Receipt of taxane chemotherapy applied in the castration-resistant setting. Priorreceipt of taxane chemotherapy in the hormone-sensitive setting is allowed

• Grade > 2 peripheral neuropathy at the time of study entry

• Has severe hypersensitivity (>= grade 3) to pembrolizumab and/or any of itsexcipients

• Has an active autoimmune disease that has required systemic treatment in the past 2years (i.e., with use of disease modifying agents, corticosteroids orimmunosuppressive drugs). Replacement therapy (e.g., thyroxine, insulin, orphysiologic corticosteroid replacement therapy for adrenal or pituitaryinsufficiency) or treatment with drugs (e.g. neomercazole, carbimazole, etc.) thatfunction to decrease the generation of thyroid hormone by a hyperfunctioning thyroidgland (e.g. in Graves? disease) is not considered a form of systemic treatment of anautoimmune disease

• Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy at aprednisone equivalent dose of > 10 mg daily or other form of immunosuppressivetherapy within 7 days prior to first dose of study drug

• Has a history of (non-infectious) ≥ grade 2 pneumonitis/interstitial lung diseasethat required steroids within past 2 years or has current ≥ grade 1pneumonitis/interstitial lung disease at the time of study enrollment..

• Has received a live vaccine or live-attenuated vaccine within 30 days prior to thefirst dose of study drug. Administration of killed vaccines is allowed.

• Participants who because of age, general medical or psychiatric condition, orphysiologic status cannot give valid informed consent

• Has clinically significant cardiovascular disease including, but not limited to:

• Uncontrolled or any New York Heart Association class 3 or 4 congestive heartfailure

• Uncontrolled angina, history of myocardial infarction, unstable angina orstroke within 6 months before study entry

• Clinically significant arrhythmias not controlled by medication. Chronic ratecontrolled or paroxysmal atrial fibrillation/flutter is not an exclusion tostudy participation

• Prior external beam radiation involving >= 25% of bone marrow or within 14 days ofstart of protocol therapy

• Major surgery within 28 days of study treatment

*Note: If participant received major surgery, they must have recovered adequatelyfrom the toxicity and/or complications from the intervention prior to starting studytreatment.

• Has an active infection requiring systemic therapy

• Has a known history of human immunodeficiency virus (HIV) (screening not required)

• Has a known history of hepatitis B (defined as hepatitis B surface antigen [HBsAg]reactive) or known active hepatitis C virus (HCV) (defined as HCV ribonucleic acid [RNA] [qualitative] is detected) infection (screening not required)

• Has a known history of active Bacillus tuberculosis (TB)

• Has known psychiatric or substance abuse disorders that would interfere withcooperation with the requirements of the trial

• Any condition that, in the opinion of the principal investigator, would impair thepatient's ability to comply with study procedures

• History of bleeding diathesis and not currently on anti-coagulation therapy thatcannot be safely discontinued for the tumor biopsy procedure