• Patients must have the ability to understand and sign an approved ICF.

• Patients must have the ability to understand and comply with all protocol requirements.

• Patients must be \>=18 years of age.

• Patients must have an ECOG performance status of 0 to 2.

• Patients must have had histological, pathological, and/or cytological confirmation of prostate cancer.

• Patients must have a positive 68Ga-PSMA-11 PET/CT scan performed within 28 days of study entry. If a patient also has soft tissue or visceral disease, it must be PSMA-positive on 68Ga-PSMA-11 PET/CT scan.

• Patients may not participate in the study if their baseline scan shows PSMA-negative disease (defined as disease that expresses PSMA at a level equal to or less than liver by visual assessment) in any of the following regions:

∙ A) One or more PSMA negative lymph nodes \>2.5 cm on short axis B) Bone metastasis with PSMA-negative soft tissues component \> 1 cm in short axis

• Note that PSMA-negative osseous metastases without a soft tissue component \>1 cm does not exclude the subject C) PSMA-negative solid organ metastases (i.e. lung, liver, adrenal glands, etc) that are PSMA-negative and ≥ 1cm in short axis

• Patients must have recovered or stabilized to =\< Grade 2 or baseline from all clinically significant toxicities related to prior prostate cancer therapy.

• Determination of disease progression on treatment prior to enrollment. Progressive disease for study entry is defined as any one or more of the following:

‣ PSA progression: minimum of two rising PSA values from a baseline measurement with an interval of \>= 1 week between each measurement. 2.0 ng/mL is the minimal starting value if PSA rise is only indication of progression.

⁃ Soft tissue or visceral disease progression as per RECIST 1.1 criteria: 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.

⁃ Bone progression: \>= 2 new lesions on bone scan.

• Patients must have adequate organ function (bone morrow reserve, hepatic function and renal function).

• Known HIV-positive patients who are healthy and have a low risk of AIDS-related outcomes are eligible. HIV testing is required.

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

• Group A Subjects: Patients must have prior orchiectomy and/or ongoing androgen-deprivation therapy, a castrate level of serum testosterone (\< 50 ng/dL or \< 1.7 nmol/L) and must have received prior cytotoxic chemotherapy and a novel androgen axis drug (e.g., abiraterone or enzalutamide). Patients must also be naïve to prior 177Lu-PSMA radioligand therapy (177Lu-PSMA-617 or 177Lu-PSMA I\&T)

• Group B Subjects (South-Africa only): Patients must have ongoing androgen deprivation therapy (ADT) and either prior orchiectomy or be medically castrate using LHRH agonists/antagonists in order to achieve adequate suppression of serum testosterone (\< 50 ng/dL) but must not have received prior cytotoxic chemotherapy or novel androgen axis drugs (e.g., abiraterone or enzalutamide). These patients are naïve to 177Lu-PSMA radioligand therapy (177Lu-PSMA-617 or 177Lu-PSMA I\&T).

• Group C Subjects: Patients must have ongoing androgen deprivation therapy (ADT) and either prior orchiectomy or be medically castrate using LHRH agonists/antagonists in order to achieve adequate suppression of serum testosterone (\< 50 ng/dL). Patients must have been treated with prior 177Lu-PSMA radioligand therapy (177Lu-PSMA-617 or 177Lu-PSMA I\&T) for at least one cycle administered greater than 6 weeks from study enrollment, and been evaluated for biochemical and radiological response to therapy. Prior exposure to ARPI and/or chemotherapy is not required.