Study of 177Lu-PSMA-617 In Metastatic Castrate-Resistant Prostate Cancer

Inclusion Criteria:

1. Patients must have the ability to understand and sign an approved informed consent form (ICF).
2. Patients must have the ability to understand and comply with all protocol requirements.
3. Patients must be \>= 18 years of age.
4. Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2.
5. Patients must have a life expectancy \>6 months.
6. Patients must have histological, pathological, and/or cytological confirmation of prostate cancer.
7. Patients must be 68Ga-PSMA-11 Positron Emission Tomography (PET)/Computed Tomography (CT) scan positive, and eligible as determined by the sponsor's central reader.
8. Patients must have a castrate level of serum/plasma testosterone (\<50 ng/dL or \<1.7 nmol/L).
9. Patients must have received at least one NAAD (such as enzalutamide and/or abiraterone).
10. Patients must have been previously treated with at least 1, but no more than 2 previous taxane regimens. A taxane regimen is defined as a minimum exposure of 2 cycles of a taxane. If a patient has received only 1 taxane regimen, the patient is eligible if: a. The patient's physician deems him unsuitable to receive a second taxane regimen (e.g. frailty assessed by geriatric or health status evaluation, intolerance, etc.).
11. Patients must have progressive mCRPC. Documented progressive mCRPC will be based on at least 1 of the following criteria:

    1. Serum/plasma PSA progression defined as 2 consecutive increases in PSA over a previous reference value measured at least 1 week prior. The minimal start value is 2.0 ng/mL.
    2. Soft-tissue progression defined as an increase \>= 20% in the sum of the diameter (SOD) (short axis for nodal lesions and long axis for non-nodal lesions) of all target lesions based on the smallest SOD since treatment started or the appearance of one or more new lesions.
    3. Progression of bone disease: evaluable disease or new bone lesions(s) by bone scan (2+2 PCWG3 criteria, Scher et al 2016).
12. Patients must have \>= 1 metastatic lesion that is present on baseline CT, MRI, or bone scan imaging obtained =\< 28 days prior to beginning study therapy.
13. Patients must have recovered to =\< Grade 2 from all clinically significant toxicities related to prior therapies (i.e. prior chemotherapy, radiation, immunotherapy, etc.).
14. Patients must have adequate organ function:

    a. Bone marrow reserve:
    * White blood cell (WBC) count \>= 2.5 x 10\^9/L (2.5 x 10\^9/L is equivalent to 2.5 x 10\^3/μL and 2.5 x K/μL and 2.5 x 10\^3/cumm and 2500/μL) OR absolute neutrophil count (ANC) \>= 1.5 x 10\^9/L (1.5 x 10\^9/L is equivalent to 1.5 x 10\^3/μL and 1.5 x K/μL and 1.5 x 10\^3/cumm and 1500/μL)
    * Platelets \>= 100 x 10\^9/L (100 x 10\^9/L is equivalent to 100 x 10\^3/μL and 100 x K/μL and 100 x 10\^3/cumm and 100,000/μL)
    * Hemoglobin \>= 9 g/dL (9 g/dL is equivalent to 90 g/L and 5.59 mmol/L) b. Hepatic:
    * Total bilirubin =\< 1.5 x the institutional upper limit of normal (ULN). For patients with known Gilbert's Syndrome =\< 3 x ULN is permitted
    * Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) =\< 3.0 x ULN OR =\< 5.0 x ULN for patients with liver metastases c. Renal:
    * Serum/plasma creatinine =\< 1.5 x ULN or creatinine clearance \>= 50 mL/min
15. Albumin \>3.0 g/dL (3.0 g/dL is equivalent to 30 g/L) \[Inclusion #16 has been removed\]

17\. HIV-infected patients who are healthy and have a low risk of AIDS-related outcomes are included in this trial.

18\. For patients who have partners of childbearing potential: Partner and/or patient must use a method of birth control with adequate barrier protection, deemed acceptable by the principle investigator during the study and for 6 months after last study drug administration.

19\. The best standard of care/ best supportive care options planned for this patient:

1. Are allowed by the protocol
2. Have been agreed to by the treating investigator and patient
3. Allow for the management of the patient without 177Lu-PSMA-617

Exclusion Criteria:

1. Previous treatment with any of the following within 6 months of randomization: Strontium-89, Samarium-153, Rhenium-186, Rhenium-188, Radium-223, hemi-body irradiation. Previous PSMA-targeted radioligand therapy is not allowed.
2. Any systemic anti-cancer therapy (e.g. chemotherapy, immunotherapy or biological therapy \[including monoclonal antibodies\]) within 28 days prior to day of randomization.
3. Any investigational agents within 28 days prior to day of randomization.
4. Known hypersensitivity to the components of the study therapy or its analogs.
5. Other concurrent cytotoxic chemotherapy, immunotherapy, radioligand therapy, or investigational therapy.
6. Transfusion for the sole purpose of making a subject eligible for study inclusion.
7. Patients with a history of Central Nervous System (CNS) metastases must have received therapy (surgery, radiotherapy, gamma knife) and be neurologically stable, asymptomatic, and not receiving corticosteroids for the purposes of maintaining neurologic integrity. Patients with epidural disease, canal disease and prior cord involvement are eligible if those areas have been treated, are stable, and not neurologically impaired. For patients with parenchymal CNS metastasis (or a history of CNS metastasis), baseline and subsequent radiological imaging must include evaluation of the brain (MRI preferred or CT with contrast).
8. A superscan as seen in the baseline bone scan.
9. Symptomatic cord compression, or clinical or radiologic findings indicative of impending cord compression.
10. Concurrent serious (as determined by the Principal Investigator) medical conditions, including, but not limited to, New York Heart Association class III or IV congestive heart failure, history of congenital prolonged QT syndrome, uncontrolled infection, known active hepatitis B or C, or other significant co-morbid conditions that in the opinion of the investigator would impair study participation or cooperation.
11. Diagnosed with other malignancies that are expected to alter life expectancy or may interfere with disease assessment. However, patients with a prior history of malignancy that has been adequately treated and who have been disease free for more than 3 years are eligible, as are patients with adequately treated non-melanoma skin cancer, superficial bladder cancer.