Adults have an interconnected lexicon in which two words are related because their referents belong to the same semantic category, because they occur in the same context, or both. This interconnection has been explored by means of the priming effect, in which people respond more rapidly to related than to unrelated words and benefit from the lexical boost when the two types of interconnections are combined. Although substantial research has reported on the memory problems of people diagnosed with Alzheimer’s disease (AD), it remains unknown whether they experience problems with related words at these levels of comprehension. This study analyzed the lexical networks of older adults with AD and typically aging (TA) adults to understand their semantic memory related to word associations. We tested combined taxonomic-thematic, purely taxonomic, and purely thematic relationships using an eye tracker to analyze fixations to a named target picture preceded by a related or unrelated prime word. Participants with TA showed a priming effect in all three types of relationships, but those with AD showed this effect only with purely thematic pairs. Words that share more than one level of relationship seem to create competition, revealing a deficit in the lexical networks of people with AD.