BACKGROUND: [Lu]Lu-PSMA-617 (Lu-PSMA-617) prolongs radiographic progression-free survival and overall survival in patients with metastatic castration-resistant prostate cancer previously treated with androgen receptor pathway inhibitor (ARPI) and taxane therapy. We aimed to investigate the efficacy of Lu-PSMA-617 in patients with taxane-naive metastatic castration-resistant prostate cancer. METHODS: In this phase 3, randomised, controlled trial conducted at 74 sites across Europe and North America, taxane-naive patients with prostate-specific membrane antigen (PSMA)-positive metastatic castration-resistant prostate cancer who had progressed once on a previous ARPI were randomly allocated (1:1) to open-label, intravenous Lu-PSMA-617 at a dosage of 7·4 GBq (200 mCi) ± 10% once every 6 weeks for six cycles, or a change of ARPI (to abiraterone or enzalutamide, administered orally on a continuous basis per product labelling). Crossover from ARPI change to Lu-PSMA-617 was allowed after centrally confirmed radiographic progression. The primary endpoint was radiographic progression-free survival, defined as the time from randomisation until radiographic progression or death, assessed in the intention-to-treat population. Safety was a secondary endpoint. This study is registered with ClinicalTrials.gov (NCT04689828) and is ongoing. In this primary report of the study, we present primary (first data cutoff) and updated (third data cutoff) analyses of radiographic progression-free survival; all other data are based on the third data cutoff. FINDINGS: Overall, of the 585 patients screened, 468 met all eligibility criteria and were randomly allocated between June 15, 2021 and Oct 7, 2022 to receive Lu-PSMA-617 (234 [50%] patients) or ARPI change (234 [50%]). Baseline characteristics were mostly similar between groups; median number of Lu-PSMA-617 cycles was 6·0 (IQR 4·0-6·0). Of patients assigned to ARPI change, 134 (57%) crossed over to receive Lu-PSMA-617. In the primary analysis (median time from randomisation to first data cutoff 7·26 months [IQR 3·38-10·55]), the median radiographic progression-free survival was 9·30 months (95% CI 6·77-not estimable) in the Lu-PSMA-617 group versus 5·55 months (4·04-5·95) in the ARPI change group (hazard ratio [HR] 0·41 [95% CI 0·29-0·56]; p<0·0001). In the updated analysis at time of the third data cutoff (median time from randomisation to third data cutoff 24·11 months [IQR 20·24-27·40]), median radiographic progression-free survival was 11·60 months (95% CI 9·30-14·19) in the Lu-PSMA-617 group versus 5·59 months (4·21-5·95) in the ARPI change group (HR 0·49 [95% CI 0·39-0·61]). The incidence of grade 3-5 adverse events was lower in the Lu-PSMA-617 group (at least one event in 81 [36%] of 227 patients; four [2%] grade 5 [none treatment related]) than the ARPI change group (112 [48%] of 232; five [2%] grade 5 [one treatment related]). INTERPRETATION: Lu-PSMA-617 prolonged radiographic progression-free survival relative to ARPI change, with a favourable safety profile. For patients with PSMA-positive metastatic castration-resistant prostate cancer who are being considered for a change of ARPI after progression on a previous ARPI, Lu-PSMA-617 may be an effective treatment alternative. FUNDING: Novartis.