A Study of 177Lu-DTPA-SC16.56 in People With Neuroendocrine Carcinomas of the Lung and Prostate

Inclusion Criteria: * Subjects with histologically proven progressive metastatic high-grade neuroendocrine carcinomas of the lung (small-cell lung cancer) and prostate (neuroendocrine prostate cancer) that has relapsed following at least 1 line of standard chemotherapy i. Prostate cancer patients will be defined by either of the following criteria: ii. The presence of chromogranin staining on tissue iii. At least two of the pathogenic mutations of PTEN, RB1, or p53 iv. Disease exclusively involving the viscera v. Disease in which the PSA is \<10 but the number of bone lesions is \>20 vi. Histologic evidence of small cell carcinoma or other stains consistent with neuroendocrine disease (on the primary disease or metastases) vii. DLL3 positivity on previously available tissue specimens * Ability to understand and willingness to sign a written informed consent document * Aged 18 years or older at the time of signing consent * Progression of disease defined by one of the following occurring within 3 months of study entry: i. At least a 20% increase in radiologically or clinically measurable disease; ii. Appearance of any new lesion; iii. For prostate cancer patients progression criteria will be per PCWG3: iv. Either v. A rising PSA over a sequence of at least 1-week intervals OR i. An increase in soft tissue disease to qualify for disease progression by RECIST 1.1 OR ii. Two new bone lesions by bone scintigraphy Patients with metastatic disease by virtue of disease exclusively evident by PSMA PET will not be eligible. All patients must have metastatic disease by evidence of standard scintigraphic or anatomic imaging in accord with PCWG3 * At least one tumor lesion on CT or MR ≥ 2 cm * ECOG performance status 0 to 2 * Women of childbearing potential and men must agree to use adequate contraception prior to study entry and for the duration of study participation. * Previous chemotherapy, immunotherapy, and/or investigational agents are allowed if completed ≥4 weeks prior to study entry. For patients who received systemic therapy prior to study entry, there must be documented progression of measurable disease since receiving systemic therapy prior to study entry. * Preserved hematological function: i. Hb ≥9.0 g/dL; ii. WBC ≥3000/mm3; iii. ANC≥1500/mm3; iv. Platelets ≥75.000/mm3 * Preserved renal function: i. Serum creatinine ≤1.7 mg/dL ii. Estimated glomerular filtration rate (eGFR) ≥30 mL/min/1.73m2 * Preserved hepatic function: i. aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 3.0 x upper limit of normal (ULN) or ≤ 5 x ULN if liver metastases are present ii. bilirubin ≤ 1.5 x ULN (unless considered due to Gilbert's syndrome or hemolysis) * Willingness to undergo baseline and follow up biopsy to obtain tissue for DLL3 IHC and genomic analyses * In order to proceed with the treatment with 177Lu-DTPA-SC16.56, patients must exhibit overexpression of DLL3, as SUVmax greater than in normal liver, in ≥80% of tumor lesions among the growing progressing lesions that are ≥2cm. Exclusion Criteria: * History of anaphylactic reaction to humanized or human antibodies * History of severe allergic reaction to X-ray contrast medium despite premedication * Prior treatment with Rova-T (rovalpituzumab) * Women who are pregnant or unwilling to discontinue breastfeeding * Spinal cord compression or symptomatic/uncontrolled epidural disease, unless treated and stable for at least 1 week prior to enrolment. * Males and females of reproductive potential who are unwilling to practice a highly effective method(s) of birth control while on study through 4 months for males and 7 months for females after receiving the therapeutic study drug. Acceptable methods of highly effective birth control include sexual abstinence (males, females); vasectomy; bilateral tubal ligation/occlusion; or a condom with spermicide (men) in combination with hormonal birth control or intrauterine device (IUD) (women) * Life expectancy \< 6 months as assessed by the treating physician. * Unresolved toxicities from prior antitumor therapy, defined per Common Terminology Criteria for Adverse Events (CTCAE), version 5.0, to to grade 1 or grade 0 or to levels dictated in the inclusion criteria. * Major surgery within 28 days of enrolment with the exception of biopsy and insertion of central venous catheter. * Uncontrolled, intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Known parenchymal brain metastases and/or carcinomatous meningitis, unless these metastases have been treated and stabilized. * Unmanageable urinary incontinence rendering the administration of 177Lu-DTPA-SC16.56 unsafe (e.g., urinary catheterization not feasible). * Other ongoing invasive malignances (i.e., not carcinomas in situ, non-mm invasive urothelial cancer, or other non-invasive tumors), and prior cancers that have been treated that have a \>30% likelihood of relapse within the next two years. * Subjects likely to not be available to complete all protocol-required study visits or procedures, and/or to comply with all required study procedures to the best of the subject's and investigator's knowledge. * Prostate cancer patients with mixed histologies (i.e., neuroendocrine and adenocarcinomas) are eligible provided that they meet all of the above eligibility criteria. * Patients for whom their clinicians believe would benefit by continuing their treatments for their disease to control any adenocarcinoma (such as ADT or other AR axis directed therapy) can and should remain on those treatments while on this protocol, if their clinician believes that it would be clinically beneficial to do so. * Concurrent chemotherapy, other radiopharmaceuticals of any type, and immunotherapy are excluded * Complementary approaches known to modulate PSA should not be taken while on this trial