Background: novel approaches are required to improve outcomes in relapsed or refractory classical Hodgkin lymphoma and non-Hodgkin lymphoma. We aimed to evaluate camidanlumab tesirine, an anti-CD25 antibody-drug conjugate, in this patient population.Methods: this was a phase 1, dose-escalation (part 1), dose-expansion (part 2), multicentre trial done in 12 hospital sites (seven in the USA and five in the UK). Adults (≥18 years old) with pathologically confirmed relapsed or refractory classical Hodgkin lymphoma or non-Hodgkin lymphoma, an Eastern Cooperative Oncology Group performance status 0-2, who had no therapies available to them with established clinical benefit for their disease stage were enrolled. Camidanlumab tesirine was administered intravenously (3-150 μg/kg) once every 3 weeks. Primary objectives were to assess dose-limiting toxicity, determine maximum tolerated dose and recommended expansion dose(s), and assess safety of camidanlumab tesirine. Safety was assessed in all treated patients; antitumour activity was assessed in patients with one or more valid baseline and post-baseline disease assessment and in those who had disease progression or died after first study-drug dose. This trial was registered with ClinicalTrials.gov, NCT02432235.Findings: between Oct 5, 2015, and Jun 30, 2019, 133 patients were enrolled (77 [58%] had classical Hodgkin lymphoma and 56 (42%) had non-Hodgkin lymphoma). Median follow-up was 9·2 months (IQR 4·2-14·3). Eight dose-limiting toxicities were reported in five (6%) of 86 patients who were evaluable; the maximum tolerated dose was not reached. The recommended doses for expansion were 30 μg/kg and 45 μg/kg for patients with classical Hodgkin lymphoma and 80 μg/kg for patients with T-cell non-Hodgkin lymphomas. No recommended doses for expansion were defined for B-cell non-Hodgkin lymphomas. Grade 3 or worse treatment-emergent adverse events (reported by ≥10% of the 133 patients) included increased γ-glutamyltransferase (20 [15%] patients), maculopapular rash (16 [12%]), and anaemia (15 [11%]); 74 (56%) patients had serious treatment-emergent adverse events, most commonly pyrexia (16 [12%]). One (1%) fatal treatment-emergent adverse event and two (2%) deaths outside the reporting period were considered at least possibly study-drug related. Antitumoural activity was seen in classical Hodgkin and non-Hodgkin lymphomas; notably in all patients with classical Hodgkin lymphoma, the overall response was 71% (95% CI 60-81).Interpretation: these results warrant evaluation of camidanlumab tesirine as a potential treatment option for relapsed or refractory lymphoma, particularly in patients with classical Hodgkin lymphoma.Funding: ADC Therapeutics.