Two findings serve as the hallmark for hemispheric specialization during lateralized lexical decision. First is an overall word advantage, with words being recognized more quickly and accurately than non-words (the effect being stronger in response latency). Second, a right visual field advantage is observed for words, with little or no hemispheric differences in the ability to identify non-words. Several theories have been proposed to account for this difference in word and non-word recognition, some by suggesting dual routes of lexical access and others by incorporating separate, and potentially independent, word and non-word detection mechanisms. We compare three previously proposed cognitive theories of hemispheric interactions (callosal relay, direct access, and cooperative hemispheres) through neural network modeling, with each network incorporating different means of interhemispheric communication. When parameters were varied to simulate left hemisphere specialization for lexical decision, only the cooperative hemispheres model showed both a consistent left hemisphere advantage for word recognition but not non-word recognition, as well as an overall word advantage. These results support the theory that neural representations of words are more strongly established in the left hemisphere through prior learning, despite open communication between the hemispheres during both learning and recall.