Radioligand Therapy After PSMA PET Guided External Beam Radiotherapy for Treating Post-Prostatectomy Patients With Biochemically Recurrent Prostate Cancer

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 in…