A Study to Evaluate the Efficacy, Safety, Pharmacokinetics and Dosimetry of [177Lu]Lu-PSMA-617 in Chinese Adult Male Patients With Progressive PSMA-Positive mCRPC

Inclusion Criteria:

* Written informed consent must be obtained before any assessment is performed.
* Participants must be Chinese male adults \>= 18 years of age.
* Participants must have histological, pathological, and/or cytological confirmation of prostate cancer.
* Participants must be \[68Ga\]Ga-PSMA-11 PET/CT scan positive, and eligible as determined by the sponsor's central reader according to the VISION read rules.
* Participants must have a castrate level of serum/plasma testosterone (\< 50 ng/dl, or \< 1.7 nmol/L).
* Participants must have received at least one ARPI (such as enzalutamide and/orabiraterone).
* Participants 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 participant has received only 1 taxane regimen, the participant is eligible if: the participants' physician deems him unsuitable to receive a second taxane regimen (e.g., frailty assessed by geriatric or health status evaluation or intolerance, etc.)
* Documented progressive mCRPC, based on at least 1 of the following criteria:

  * Serum/plasma PSA progression defined as 2 consecutive increases in PSA measured at least 1 week apart, the minimal start value is 2.0 ng/ml
  * Soft-tissue progression defined based on PCWG3-modified RECIST v1.1 (Eisenhauer et al 2009, Scher et al 2016)
  * Progression of bone disease: two new lesions; only positivity on the bone scan defines metastatic disease to bone (PCWG3 criteria (Scher et al 2016)
* Participants must have \>= 1 metastatic lesion that is present on baseline CT, MRI or bone scan imaging obtained =\< 21 days prior to enrollment via central reading.

  * In main part: participant must have at least one measurable lesion by PCWG3-modified RECIST v1.1 via central reading
* Participants must have adequate organ function:

  * Bone marrow reserve:
  * White blood cell (WBC) count \>= 2.5 × 109/L OR absolute neutrophil count (ANC) \>= 1.5 × 109/L
  * Platelets \>=100 × 109/L
  * Hemoglobin \>= 9 g/dL
  * Hepatic:
  * Total bilirubin =\< 1.5 x the institutional upper limit of normal (ULN). For participants with known Gilbert's Syndrome =\< 3 × ULN is permitted
  * Alanine aminotransferase (ALT) or aspartate aminotransferase (AST) =\< 3.0 × ULN OR =\< 5.0 × ULN for participants with liver metastases
  * Renal:
  * eGFR \>= 50 mL/min/1.73m2 using the Modification of Diet in Renal Disease (MDRD) equation
* Albumin \>3.0 g/dL.

Exclusion Criteria:

* Previous treatment with Strontium-89, Samarium-153, Rhenium-186, Rhenium-188, Radium-223 or hemi-body irradiation.
* Previous PSMA-targeted radioligand therapy.
* Any systemic anti-cancer therapy (e.g. chemotherapy, immunotherapy or biological therapy \[including monoclonal antibodies\], APRI is not included) within 28 days prior to day of enrollment.
* Any investigational agents (e.g. poly adenosine diphosphate-ribosyl polymerase inhibitors \[PARPi\]) within 28 days prior to day of enrollment.
* History of hypersensitivity to any of the study drugs or its excipients or to drugs of similar chemical classes.
* Other concurrent cytotoxic chemotherapy, immunotherapy, radioligand therapy, or investigational therapy.
* Transfusion for the sole purpose of making a subject eligible for study inclusion.
* Participants with a history of central nervous system (CNS) metastases who are neurologically unstable, symptomatic, or receiving corticosteroids for the purpose of maintaining neurologic integrity.

  * Participants with CNS metastases are eligible if received therapy (surgery, radiotherapy, gamma knife), asymptomatic and neurologically stable without corticosteroids.
  * Participants with epidural disease, canal disease and prior cord involvement are eligible if those areas have been treated, are stable, and not neurologically impaired.
* Symptomatic spinal cord compression, or clinical or radiologic findings indicative of impending cord compression.