This is a single-arm, open-label, Phase I/II clinical study designed to evaluate the safety, tolerability, pharmacokinetics, dosimetry, pharmacodynamics, and preliminary efficacy of Gallium \[68Ga\] PSMA-0057 Injection and Lutetium \[177Lu\] PSMA-0057 Injection as an integrated theranostic regimen in patients with PSMA-positive metastatic castration-resistant prostate cancer (mCRPC). The study consists of a Phase I dose-escalation phase to determine the maximum tolerated dose (MTD) and/or recommended Phase II dose (RP2D) of 177Lu-PSMA-0057, followed by a Phase II dose-expansion phase to further evaluate preliminary antitumor efficacy and confirm safety and pharmacologic profiles. Eligible participants will receive 68Ga-PSMA-0057 for PET imaging and 177Lu-PSMA-0057 for radioligand therapy. Key objectives include characterization of safety, tolerability, pharmacokinetics, dosimetry, pharmacodynamics, and preliminary therapeutic activity.