177-Lutetium-PSMA Before Stereotactic Body Radiotherapy for the Treatment of Oligorecurrent Prostate Cancer, The LUNAR Study

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