This phase II trial tests whether 177-Lutetium-PSMA given before stereotactic body radiotherapy (SBRT) works to improve cancer control rate in patients with 1-5 prostate cancer tumors that have come back after prior treatment (oligorecurrent). Radioactive drugs, such as 177-Lutetium-PSMA, may carry radiation directly to tumor cells and not harm normal cells. SBRT uses special equipment to position a patient and deliver radiation to tumors with high precision. This method may kill tumor cells with fewer doses over a shorter period and cause less damage to normal tissue. Giving 177-Lutetium-PSMA before SBRT may make the SBRT more effective.

PRIMARY OBJECTIVE:

I. To assess progression-free survival for men with oligorecurrent prostate cancer after stereotactic body radiotherapy (SBRT) versus SBRT plus neoadjuvant lutetium Lu-177 PNT2002 (177Lu-PNT2002), with progression defined on the basis of prostate-specific membrane antigen positron emission tomography/computerized tomography (PSMA PET/CT) scans obtained at standard intervals (12 months and 24 months post-SBRT) or at the time of prostate-specific antigen (PSA)-based biochemical progression, or initiation of salvage therapy or death.

SECONDARY OBJECTIVES:

I. To evaluate disease burden of disease (including local control of irradiated lesions and presence of other disease) on a PSMA PET/CT obtained 24 months after SBRT of SBRT versus SBRT + 177Lu-PNT2002 in patients with oligometastatic disease who have not progressed by that point.

II. To assess physician-scored toxicity (Common Terminology Criteria for Adverse Events version 5.0 [CTCAE v 5.0]) of SBRT versus SBRT + 177Lu-PNT2002 in patients with oligometastatic disease.

III. To assess patient-reported quality of life (based on the brief pain inventory scale) after SBRT versus SBRT + 177Lu-PNT2002 in patients with oligometastatic disease.

IV. To assess androgen deprivation therapy (ADT)-free survival after SBRT versus SBRT + 177Lu-PNT2002 in patients with oligometastatic disease.

V. To determine local control of irradiated lesion at 12 months after SBRT versus SBRT + 177Lu-PNT2002 in patients with oligometastatic disease (based on a scheduled PSMA-PET).

VI. To assess time to locoregional progression, time to distant progression, time to new metastasis, and duration of response after SBRT versus SBRT + 177Lu-PNT2002 in patients with oligometastatic disease (based on standard of care imaging).

CORRELATIVE OBJECTIVES:

I. To enumerate circulating tumor cells (CTCs) and circulating tumor deoxyribonucleic acid (ctDNA) at baseline, 3 months, 6 months, and 12 months after SBRT.

II. To quantitatively sequence T-cell receptor (TCR) repertoires using peripheral blood monocytes at baseline, 3 months, 6 months, and 12 months after SBRT.

III. To perform radiomics analysis on PSMA PET/CT scans performed at +12 months (mo.), +24 months post-SBRT, or at time of progression.

OUTLINE: Patients are randomized to 1 of 2 arms.

ARM 1: Beginning on day 1, patients undergo SBRT to all lesions for 1, 3, or 5 treatment doses (fractions) over the span of 10-20 days in the absence of disease progression or unacceptable toxicity.

ARM 2: Patients receive 177Lu-PNT2002 intravenously (IV) over 1-10 minutes on days -112 and -56 in the absence of disease progression or unacceptable toxicity. Beginning on day 1, patients then undergo SBRT to all lesions for 1, 3, or 5 treatment doses (fractions) over the span of 10-20 days in the absence of disease progression or unacceptable toxicity.

After completion of study treatment patients are followed up at 1, 3, 6, 9, and 12 months, then every 6 months until 60 months of total follow-up.

Inclusion Criteria:

• Oligorecurrent prostate cancer as determined by the presence of 1-5 asymptomatic lesions outside the prostate or prostate bed identified on PSMA PET/CT by local readers
• Age >= 18 years
• Eastern Cooperative Oncology Group (ECOG) performance status =< 2
• No indication for urgent or emergent radiation
• Histologic confirmation of prostate adenocarcinoma (histology from original treatment acceptable)
• White blood cell count >= 2.5 × 10^9/L
• Platelets >= 100 × 10^9/L
• Hemoglobin >= 9 g/dL
• Total bilirubin =< 1.5 × institutional upper limit of normal (ULN); or up to 3 × ULN if known history of Gilbert's syndrome
• Alanine aminotransferase or aspartate aminotransferase =< 3.0 × ULN or =< 5.0 × ULN for patients with liver metastases
• Serum creatinine =< 1.5 × ULN or creatinine clearance >= 50 mL/min
• Serum albumin > 3.0 g/dL
• Partner and patient must use a method of birth control with adequate barrier protection, deemed acceptable by the principal investigator during the study and for 3 months after last study drug administration
• Ability to understand, and willingness to sign, the written informed consent

Exclusion Criteria:

• Patients with neuroendocrine or small cell carcinoma of the prostate
• Patients with castrate-resistant disease (i.e., PSA > 0.5 ng/mL with serum testosterone < 150 ng/dL)
• Patients who received androgen deprivation therapy within 6 months of trial enrollment
• Concurrent systemic therapy for a solid organ malignancy
• Spinal cord compression
• Inability to lie flat
• Known hypersensitivity to components of 177Lu-PNT2002
• Serum creatinine > 1.5 × ULN or creatinine clearance < 50 mL/min
• Total bilirubin > 1.5 × ULN or > 3.0 × ULN if known history of Gilbert's syndrome
• Alanine aminotransferase or aspartate aminotransferase > 3 × ULN (or 5 × ULN for patients with known liver metastases)
• De novo oligometastatic disease