In recent years, it has become clear that attention plays an important role in spoken word production. Some of this evidence comes from distributional analyses of reaction time (RT) in regular picture naming and picture-word interference. Yet we lack a mechanistic account of how the properties of RT distributions come to reflect attentional processes and how these processes may in turn modulate the amount of conflict between lexical representations. Here, we present a computational account according to which attentional lapses allow for existing conflict to build up unsupervised on a subset of trials, thus modulating the shape of the resulting RT distribution. Our process model resolves discrepancies between outcomes of previous studies on semantic interference. Moreover, the model's predictions were confirmed in a new experiment where participants' motivation to remain attentive determined the size and distributional locus of semantic interference in picture naming. We conclude that process modeling of RT distributions importantly improves our understanding of the interplay between attention and conflict in word production. Our model thus provides a framework for interpreting distributional analyses of RT data in picture naming tasks.