Dose Optimization and Diagnostic Performance in Prostate Cancer (SPARROW [Staging Prostate Cancer With Advanced RM2 Radiotracer Oncologic Workup])

Inclusion Criteria: Participants must meet all of the criteria below as defined to be enrolled in the study. 1. Participants must be male and ≥18 years old or defined as adults per applicable local laws and regulations, at the time of signing the informed consent. 2. Participants who are sexually active must agree to the following during the study and for 7 days after last administration of study drug: 1. Use 2 highly effective contraceptive methods when engaging in sexual intercourse with partners who are pregnant or of childbearing potential (Appendix 2). 2. Refrain from donating sperm. 3. Participants who are claustrophobic must be willing to take an anti-anxiety medication prescribed by their physician one hour prior to the scan. 4. Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2. 5. Adequate organ function, 5. Adequate organ function, defined as follows: Bone marrow reserve: * White blood cell count ≥ 2.5 × 109/L OR absolute neutrophil count (ANC) ≥ 1.5 × 109/L * Platelets ≥ 100 × 109/L * Platelets ≥ 100 × 109/L Liver function: * Total bilirubin ≤ 1.5 × institutional upper limit of normal (ULN). For participants with known Gilbert's syndrome, ≤ 3 × ULN is permitted. * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 3.0 × ULN Renal function: * Estimated glomerular filtration rate (eGFR \>60 mL/min/1.73 m2) calculated using the CKD EPI 2021 creatinine equation (race-neutral).80 The eGFR must be derived from a serum creatinine value measured at Screening * Albumin ≥ 30 g/L. 6. All participants must have histological, pathological, and/or cytological confirmation of adenocarcinoma of the prostate and meet either disease population based on the phase specific criteria below, as applicable. 1. Newly Diagnosed Prostate Cancer (Phase 2 and 3): high-risk prostate cancer as defined by the National Comprehensive Cancer Network (NCCN) Guidelines, Version 5.2026 (clinical stage ≥T3a, or PSA \>20 ng/mL, or Grade Group 4-5 \[Gleason score 8-10\]), and planned treatment with radical prostatectomy plus pelvic lymph node dissection (RP+PLND) or 2. Biochemically Recurrent Prostate Cancer (Phase 2 Only) Post-definitive-therapy disease with suspected recurrence, based on elevated prostate-specific antigen (PSA) following definitive therapy, meeting one of the following criteria: * Post-radical prostatectomy (RP): Detectable or rising serum PSA ≥0.2 ng/mL with a confirmatory serum PSA ≥0.2 ng/mL, consistent with American Urological Association (AUA) recommendations; or * Post-radiation therapy (RT), cryotherapy, or brachytherapy: Increase in serum PSA ≥2.0 ng/mL above the nadir, consistent with the American Society for Therapeutic Radiology and Oncology (ASTRO)-Phoenix consensus definition. 7. Must be able and willing to comply with all study requirements and treatments as well as the timing and nature of required assessments. Exclusion Criteria: Participants meeting any of the following exclusion criteria are not eligible for this study. 1. Participants that have been administered any high-energy (\> 300 KeV) gamma-emitting radioisotope within 5 physical half-lives, or any intravenous (IV) iodinated contrast medium within 24 hours, or any high-density oral contrast medium (oral water contrast is acceptable) within 5 days prior to study drug injection. 2. Participants are excluded if they have received any other prior anti-cancer therapy (including radioligand therapy) or investigational agent within ≤28 days (or 5 half-lives, whichever is shorter) prior to the first dose of study treatment. Note: Prior external beam radiation therapy (EBRT) is permitted for Phase 2 participants with BCR PCa only. 3. Participants who are planning to undergo alternate medical procedures for prostate cancer from the time of dosing (Day 1) to surgery. 4. History of malignancy other than prostate cancer that, in the opinion of the Investigator, is expected to alter life expectancy or may interfere with study assessments, including imaging interpretation or histopathological evaluation. Participants with adequately treated nonmelanoma skin cancer, superficial bladder cancer, or other malignancies that have been disease free for more than 2 years are eligible. 5. Any medical, psychological, familial, sociological, or geographical condition that, in the opinion of the Investigator, may compromise the participant's ability to comply with study requirements, undergo study procedures, or result in the collection of reliable data. 6. Active participation in another clinical study at the time of screening for this study. 7. Known contraindications or hypersensitivity to \[68Ga\]-LNTH-2401 and/or excipients. 8. Clinical evidence or history of central nervous system metastases. 9. Clinically significant cardiovascular disease, that in the opinion of the Investigator may pose an unacceptable risk to the participant or interfere with study assessments. This includes any of the following: 1. recent myocardial infarction or arterial thrombotic events (in the past 6 months); current history of New York Heart Association (NYHA) Class III or IV heart failure, uncontrolled angina, or severe uncontrolled ventricular arrhythmias; or bradycardia or left ventricular ejection fraction measurement of 2. history of additional risk factors for Torsade de pointes (e.g., heart failure, hypokalemia, congenital long QT syndrome, and/or familial history of prolonged QT syndrome) or taking medication known to cause QT/QTc prolongation; or marked baseline prolongation of the QT/QTc interval (e.g., repeated demonstration of a QTc interval, calculated with Fridericia's correction, \>450 ms). 10. Treatment-related adverse events from prior or concurrent therapies that have not resolved to grade ≤1 according to the CTCAE Version 6.0. 11. Imaging evidence of metastatic disease that precludes surgical indication.