Key Inclusion Criteria:  ECOG performance status:  Post-taxane population only: 0 to 2. Pre-taxane population only: 0 to 1. Participants must have a previous histological, pathological, and/or cytological confirmation of prostate cancer. Participants must have a positive 68Ga-PSMA-11 PET/CT scan, as determined by the sponsor's central reader, before the enrollment to 177Lu-PSMA-617 treatment period. Participants must have a castrate level of serum/plasma testosterone (<50 ng/dL or <1.7 nmol/L). Post-taxane population only: Participants must have received at least one ARDT (for example enzalutamide, abiraterone, apalutamide, or darolutamide, etc.) in either the hormone-sensitive/castrate-resistant or non-metastatic/metastatic prostate cancer setting. Pre-taxane population only: Participants must have received one prior approved ARDT (for example, abiraterone, enzalutamide, darolutamide, or apalutamide, etc.) and have documented progression on therapy and be a candidate for additional treatment with an alternate ARDT as assessed by the treating physician  Post-taxane population only: Participants must have been previously treated with at least 1, but no more than 2 prior 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 :  a. The participant's physician deems him unsuitable to receive a second taxane regimen (e.g., frailty assessed by geriatric or health status evaluation or intolerance, etc.).  Participants must have progressive mCRPC. Documented progressive mCRPC will be based on at least 1 of the following criteria:  Serum 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. 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. Progression of bone disease: evaluable disease or new bone lesions(s) by bone scan (PCWG3 criteria, Scher et al 2016). Participants must have at least one measurable lesion per PCWG3-modified RECIST v1.1 on CT or MRI.  Key Exclusion Criteria:  Previous treatment with any of the following within 6 months of the enrollment: Strontium-89, Samarium-153, Rhenium-186, Rhenium-188, Radium-223, hemi-body irradiation. Previous PSMA-targeted therapy is not allowed. Post-taxane population: Any systemic anti-cancer therapy (e.g. chemotherapy, immunotherapy or biological therapy [including monoclonal antibodies], ARDT is not included) within 28 days prior to day of the enrollment. Pre-taxane population: Prior treatment with cytotoxic chemotherapy for castration resistant or castrate sensitive prostate cancer (e.g., taxanes, platinum, estramustine, vincristine, methotrexate, etc.), immunotherapy or biological therapy [including monoclonal antibodies]) [Note: Taxane exposure (maximum 6 cycles) in the adjuvant or neoadjuvant setting is allowed if 12 months have elapsed since completion of this adjuvant or neoadjuvant therapy] Known hypersensitivity to the components of 177Lu-PSMA-617, 68Ga-PSMA-11 or excipients or to drugs of similar classes. Other concurrent cytotoxic chemotherapy, immunotherapy, radioligand therapy, PARP inhibitors, or AKT inhibitors or investigational therapy. Participants with a history of 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. Symptomatic cord compression, or clinical or radiologic findings indicative of impending cord compression.