BACKGROUND: The TheraP study reported improved prostate-specific antigen responses with lutetium-177 [Lu]Lu-PSMA-617 versus cabazitaxel in men with metastatic castration-resistant prostate cancer progressing after docetaxel. In this Article, we report the secondary outcome of overall survival with mature follow-up, and an updated imaging biomarker analysis. We also report the outcomes of participants excluded due to ineligibility on gallium-68 [Ga]Ga-PSMA-11 and 2-[F]fluoro-2-deoxy-D-glucose (2-[F]FDG) PET-CT. METHODS: TheraP was an open-label, randomised phase 2 trial at 11 centres in Australia. Eligible participants had metastatic castration-resistant prostate cancer progressing after docetaxel, and PET imaging with [Ga]Ga-PSMA-11 and 2-[F]FDG that showed prostate-specific membrane antigen (PSMA)-positive disease and no sites of metastatic disease with discordant 2-[F]FDG-positive and PSMA-negative findings. Participants were randomly assigned (1:1) to treatment with [Lu]Lu-PSMA-617 (every 6 weeks for a maximum of six cycles; starting at 8·5 GBq, decreasing by 0.5 GBq to 6·0 GBq for the sixth cycle) versus cabazitaxel (20 mg/m every 3 weeks, maximum of ten cycles). Overall survival was analysed by intention-to-treat and summarised as restricted mean survival time (RMST) to account for non-proportional hazards, with a 36-month restriction time corresponding to median follow-up. This trial is registered with ClinicalTrials.gov, NCT03392428, and is complete. FINDINGS: 291 men were registered from Feb 6, 2018, to Sept 3, 2019; after study imaging, 200 were eligible and randomly assigned to treatment with [Lu]Lu-PSMA-617 (n=99) or cabazitaxel (n=101). After completing study treatment, 20 (20%) participants assigned to cabazitaxel and 32 (32%) assigned to [Lu]Lu-PSMA-617 were subsequently treated with the alternative regimen. After a median follow-up of 35·7 months (IQR 31·1 to 39·2), 77 (78%) participants had died in the [Lu]Lu-PSMA-617 group and 70 (69%) participants had died in the cabazitaxel group. Overall survival was similar among those assigned to [Lu]Lu-PSMA-617 versus those assigned to cabazitaxel (RMST 19·1 months [95% CI 16·9 to 21·4] vs 19·6 months [17·4 to 21·8]; difference -0·5 months [95% CI -3·7 to 2·7]; p=0·77). No additional safety signals were identified with the longer follow-up in this analysis. 80 (27%) of 291 men who were registered after initial eligibility screening were excluded after [Ga]Ga-PSMA-11 and 2-[F]FDG PET. In the 61 of these men with follow-up available, RMST was 11·0 months (95% CI 9·0 to 13·1). INTERPRETATION: These results support the use of [Lu]Lu-PSMA-617 as an alternative to cabazitaxel for PSMA-positive metastatic castration-resistant prostate cancer progressing after docetaxel. We did not find evidence that overall survival differed between the randomised groups. Median overall survival was shorter for men who were excluded because of low PSMA expression or 2-[F]FDG-discordant disease. FUNDING: Australian and New Zealand Urogenital and Prostate Cancer Trials Group, Prostate Cancer Foundation of Australia, Endocyte (a Novartis company), Australian Nuclear Science and Technology Organization, Movember, It's a Bloke Thing, CAN4CANCER, and The Distinguished Gentleman's Ride.