Flexible language use requires coordinated functioning of two systems: conceptual representations and control. The interaction between the two systems can be observed when people are asked to match a word to a picture. Participants are slower and less accurate for related word-picture pairs (word: banana, picture: apple) relative to unrelated pairs (word: banjo, picture: apple). The mechanism underlying interference however is still unclear. We analyzed word-picture matching (WPM) performance of patients with stroke-induced lesions to the left-temporal (N = 5) or left-frontal cortex (N = 5) and matched controls (N = 12) using the drift diffusion model (DDM). In DDM, the process of making a decision is described as the stochastic accumulation of evidence towards a response. The parameters of the DDM model that characterize this process are decision threshold, drift rate, starting point and non-decision time, each of which bears cognitive interpretability. We compared the estimated model parameters from controls and patients to investigate the mechanisms of WPM interference. WPM performance in controls was explained by the amount of information needed to make a decision (decision threshold): a higher threshold was associated with related word-picture pairs relative to unrelated ones. No difference was found in the quality of the evidence (drift rate). This suggests an executive rather than semantic mechanism underlying WPM interference. Both patients with temporal and frontal lesions exhibited both increased drift rate and decision threshold for unrelated pairs relative to related ones. Left-frontal and temporal damage affected the computations required by WPM similarly, resulting in systematic deficits across lexical-semantic memory and executive functions. These results support a diverse but interactive role of lexical-semantic memory and semantic control mechanisms.