Patients with lesions in the left prefrontal cortex (PFC) have been shown to be impaired in lexical selection, especially when interference between semantically related alternatives is increased. To more deeply investigate which computational mechanisms may be impaired following left PFC damage due to stroke, a psychometric modelling approach is employed in which we assess the cognitive parameters of the patients from an evidence accumulation (sequential information sampling) modelling of their response data. We also compare the results to healthy speakers. Analysis of the cognitive parameters indicates an impairment of the PFC patients to appropriately adjust their decision threshold, in order to handle the increased item difficulty that is introduced by semantic interference. Also, the modelling contributes to other topics in psycholinguistic theory, in which specific effects are observed on the cognitive parameters according to item familiarization, and the opposing effects of priming (lower threshold) and semantic interference (lower drift) which are found to depend on repetition. These results are developed for the blocked-cyclic picture naming paradigm, in which pictures are presented within semantically homogeneous (HOM) or heterogeneous (HET) blocks, and are repeated several times per block. Overall, the results are in agreement with a role of the left PFC in adjusting the decision threshold for lexical selection in language production.