Study of PSMA-targeted Therapy and Androgen Receptor Suppression in Low-volume Metastatic ProstatE Cancer: SPARKLE Trial

Inclusion Criteria: * Male patients aged 18 years or older * Signed informed consent must be obtained prior to participation in the study * Histologically confirmed adenocarcinoma of the prostate * Prior treatment with radical prostatectomy or radiation therapy for localized disease is required * Prior treatment with ADT or androgen receptor pathway inhibitor (ARPI) or cytotoxic chemotherapy is permitted if: * The last treatment \> 12 months from enrollment on the trial * The duration of treatment is less than 3 months and no evidence of disease progression on treatment * Disease detected on PSMA PET/CT scan \[PSMA-avid low volume metastasis (LVM)\]. Patients with standardized uptake value maximum (SUVMax) lesion/liver \>1 \[molecular imaging PSMA (miPSMA) score of 2\] or lesion/parotid \> 1 (miPSMA score of 3) would be included. PET scanners used in the study will comply with current guidelines established by the European Association of Nuclear Medicine (EANM) Research Limited (Ltd) (EARL) for harmonizing PET/CT image acquisition and reconstruction * Patients with hormone sensitive low volume metastatic disease (LVM); either de novo metastatic or recurrent disease. LVM, as assessed on PSMA PET/CT is defined as: * =\< 10 total metastatic spots * Lymph nodes with short axis of =\< 2.5 cm * Total tumor volume (TTV) \< 200 mL * =\< 4 bone metastases * No brain or liver metastases * Eastern Cooperative Oncology Group (ECOG) performance 0 - 2 * Hemoglobin \>= 9 g/dL * Platelet count \>= 100,000/mm\^3 * Absolute neutrophil count \>= 1,500/mm\^3 * Serum bilirubin =\< 1.5 x upper limit of normal (ULN) * Alanine aminotransferase (ALT)/aspartate aminotransferase (AST) =\< 2.5 x ULN * Serum creatinine =\< 1.5 x ULN or an estimated glomerular filtration rate (eGFR) \>= 50 mL/min/1.73m\^2 * Able to start therapy within 28 days of screening * Expected life expectancy \> 6 months Exclusion Criteria: * PSMA-undetectable disease defined as rising prostate specific antigen (PSA) with absence of PSMA-positive lesions in PSMA PET/CT imaging * PSMA-negative disease defined as lesions detected on imaging that are deemed concerning for active cancer metastasis with PSMA SUVmax less than liver and meeting specific size criteria: lymph nodes with short axis of \>= 2.5 cm, visceral lesions with a solid appearance (soft tissue density) \>= 1 cm, and bone metastases with a measurable soft tissue component \>= 1 cm * Patient with in-field failure (disease recurrence in prostate bed after primary definitive prostatectomy or radiotherapy) * Patient with spinal metastatic disease-causing cord compression * Patient with prior disease progression on ADT \[castration resistance prostate cancer (CRPC)\] * Prior treatment with ADT or cytotoxic chemotherapy or ARPI within less than 12 months from enrollment on the trial * Prior treatment with ADT or ARPI or cytotoxic chemotherapy is permitted only if more than 3 months treatment duration and no evidence of disease progression on treatment * Patients with severe \[Common Terminology Criteria for Adverse Events (CTCAE) grade \> 2\] xerostomia * Patients with well documented history of myelosuppression or renal disease that might impair their participation in the trial per medical advice * Diagnosed with other malignancies that are expected to alter life expectancy or may interfere with disease assessment. However, participants with a prior history of malignancy that has been adequately treated non-melanoma skin cancer, superficial bladder cancer are eligible * Estimated life expectancy \< 6 months * Concurrent serious medical co-morbidities as determined by study investigator and expected to impair participation in the study * Subjects with female partners of reproductive potential are required to use effective, medically acceptable methods of birth control (e.g., spermicide in conjunction with a barrier such as a condom or sexual abstinence) while on this study, and for 14 weeks after the last dose of 177Lu-PSMA-617