This phase I trial tests the safety, side effects and best dose of radioligand therapy (lutetium Lu 177 PSMA-10.1 [177Lu-rhPSMA-10.1]) after prostate specific membrane antigen (PSMA) positron emission tomography (PET)-guided external beam radiotherapy in treating post-prostatectomy patients with prostate cancer that has come back after a period of improvement (recurrent). In this study, radioligand therapy is a radioactive drug called 177Lu-rhPSMA-10.1. It works by binding to PSMA-expressing prostate tumor cells and delivering the radioactive portion of the drug directly to the tumor cells while not harming normal cells. Radiation therapy such as external beam radiotherapy uses high energy x-rays to kill tumor cells and shrink tumors. Giving radioligand therapy with PSMA PET-guided external beam radiotherapy may kill more tumor cells in post-prostatectomy patients with biochemically recurrent prostate cancer.

PRIMARY OBJECTIVES:

I. Demonstrate the safety and feasibility of treating radiotherapy (RT) prostate cancer patients via addition of lutetium Lu 177 PSMA-10.1 (177Lu-rhPSMA-10.1) in a selected post-prostatectomy population.

II. Analyze dosimetry of radioligand therapy (RLT) after each cycle of 177Lu-rhPSMA-10.1.

EXPLORATORY OBJECTIVE:

I. Determine the feasibility of and develop preliminary data in the correlation of circulating tumor circulating tumor deoxyribonucleic acid (ctDNA) at baseline, after RT, and RLT.

OUTLINE: This is a dose-escalation study of 177Lu-rhPSMA-10.1.

Patients undergo external beam radiation therapy (EBRT) followed by 177Lu-rhPSMA-10.1 intravenously (IV) on study. Patients also receive flotufolastat F-18 (rhPSMA-7.3) IV with positron emission tomography (PET)/computed tomography (CT) at screening and undergo single-photon emission computed tomography (SPECT)-CT and collection of blood samples on study.

Patients follow up 6 weeks after the last 177Lu-rhPSMA-10.1 administration.

Inclusion Criteria:

• Adenocarcinoma of the prostate, post radical prostatectomy with detectable prostate specific antigen (PSA)
• Clinical PSMA PET/CT obtained, with findings of pelvic uptake only (prostate bed, pelvic lymph node uptake, or both)
• Eastern Cooperative Oncology Group (ECOG)/Zubrod performance status of 0-2
• Age over 18

Exclusion Criteria:

• Contraindications to radiotherapy (including active inflammatory bowel disease or prior pelvic radiotherapy or prior RLT)

• Risk factors for Lu-rhPSMA radioligand therapy (Baseline >= grade 2 myelosuppression, renal insufficiency [glomerular filtration rate (GFR) < 60 mL/min], or xerostomia)

• Definitive findings of systemic metastasis prior imaging (if obtained) or biopsy (if obtained)

• Unacceptable medical or radiation safety risk

• Unmanageable urinary tract obstruction or hydronephrosis; patients with diagnosed or who are at high risk of urinary retention

• GFR < 60 mL/min or creatinine > 1.5-fold upper limit of normal (ULN)

• Liver enzymes > 5-fold ULN

• Total white cell count less than 2.5 x 10^9 /L

• Platelet count less than 75 x 10^9 /L

• Any baseline grade 2 or above myelosuppression, nephrotoxicity, hepatotoxicity, xerostomia, or gastrointestinal (GI) toxicity

• Severe acute co-morbidity, defined as follows:

  • Unstable angina and/or congestive heart failure requiring hospitalization in the last 3 months
  • Transmural myocardial infarction within the last 6 months
  • Acute bacterial or fungal infection requiring intravenous antibiotics at the time of registration
  • Chronic obstructive pulmonary disease exacerbation or other respiratory illness requiring hospitalization or precluding study therapy at the time of registration
  • Acquired immune deficiency syndrome (AIDS) based upon current Centers for Disease Control and Prevention (CDC) definition; note, however, that human immunodeficiency virus (HIV) testing is not required for entry into this protocol. The need to exclude patients with AIDS from this protocol is necessary because the treatments involved in this protocol may be significantly immunosuppressive. Protocol-specific requirements may also exclude immunocompromised patients