Schedule De-Escalation of 177Lu-PSMA-617 for the Treatment of Metastatic Castrate Resistant Prostate Cancer

Inclusion Criteria: * REGISTRATION INCLUSION CRITERIA * Scheduled at Mayo Clinic Rochester for therapy with 177Lu PSMA-617 * PSMA positive metastatic castration resistant prostate cancer (68Ga and 18F PSMA PET will be considered equivalent for eligibility) , defined by molecular imaging prostate specific membrane antigen (miPSMA) score \>= 2 on Mayo PET report, including interpretation of outside PET or consensus review of PET by nuclear therapy tumor board note in the patient chart * Willingness to provide mandatory blood draws for correlative research. (This requirement is waived for patients enrolling after receiving cycle 1 of 177Lu PSMA-617,and achieving a near complete response on post therapy SPECT, as these patients will not be able to provide a pre-treatment baseline blood sample.) * Provide written informed consent * Ability to complete questionnaire(s) by themselves or with assistance * Willing to return to enrolling institution for follow-up (during the active monitoring phase of the study) * RANDOMIZATION INCLUSION CRITERIA * Lesions with uptake equal to or above liver on cycle 1 post therapy SPECT, demonstrating that a near complete response on follow up post-therapy scan represents response, rather than sensitivity differences between SPECT and pre-treatment PET * Near-complete response on post-therapy SPECT following any of cycles 2-5 of 177Lu PSMA-617. Near-complete response will be defined as no lesions with SUV max above the mean standard uptake value (SUV) of a representative 2cm spherical region of interest in the central right hepatic lobe, as determined by a nuclear medicine trained radiologist * No toxicity that would indicate withholding or reducing dose of the next scheduled cycle of 177Lu PSMA-617 per prescribing information * Hemoglobin (Hgb) ≥ 8 g/dL * Platelets ≥ 75,000/mm\^3 * Neutrophils ≥ 100/mm\^3 * Estimated glomerular filtration rate (eGFR) \< 50 mL/min \*body surface area (BSA) using Cockcroft-Gault formula OR * Creatinine ≤ 1.5 x upper limit of normal * Aspartate transferase (AST) or alanine transaminase (ALT) ≤ 3 x upper limit of normal * No other unacceptable toxicity in the clinical judgement of the investigators * RE-REGISTRATION INCLUSION CRITERIA (CROSSOVER TO COMPLETION UPON FIRST PROGRESSION OF PATIENTS RANDOMIZED TO TREATMENT PAUSE) * First progression in patients randomized to pause treatment * PSMA avid lesions on PSMA PET (miPSMA score ≥ 2 following first progression) Exclusion Criteria: * REGISTRATION EXCLUSION CRITERIA * Another active malignancy requiring therapy such as radiation, chemotherapy, or immunotherapy * Receiving any other investigational agent which would be considered as a treatment for the prostate cancer * Failure to recover from acute, reversible effects of prior therapy regardless of interval since last treatment * EXCEPTION: Grade 1 peripheral (sensory) neuropathy that has been stable for at least 3 months since completion of prior treatment * Uncontrolled intercurrent non-cardiac illness including, but not limited to: * Ongoing or active infection * Psychiatric illness/social situations * Dyspnea at rest due to complications of advanced malignancy or other disease that requires continuous oxygen therapy * Any other conditions that would limit compliance with study requirements * Any of the following because this study involves: An investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown * Persons able to father a child who are unwilling to employ adequate contraception * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens * History of myocardial infarction ≤6 months, or congestive heart failure requiring use of ongoing maintenance therapy for life-threatening ventricular arrhythmias * RE-REGISTRATION EXCLUSION CRITERIA * Serious adverse effect