An emerging area of research in cognitive science is the utilization of networks to model the structure and processes of the mental lexicon in healthy and clinical populations, like aphasia. Previous research has focused on only one type of word similarity at a time (e.g., semantic relationships), even though words are multi-faceted. Here, we investigate lexical retrieval in a picture naming task from people with Broca's and Wernicke's aphasia and healthy controls by utilizing a multiplex network structure that accounts for the interplay between multiple semantic and phonological relationships among words in the mental lexicon. Extending upon previous work, we focused on the global network measure of closeness centrality which is known to capture spreading activation, an important process supporting lexical retrieval. We conducted a series of logistic regression models predicting the probability of correct picture naming. We tested whether multiplex closeness centrality was a better predictor of picture naming performance than single-layer closeness centralities, other network measures assessing local and meso-scale structure, psycholinguistic variables and group differences. We also examined production gaps, or the difference between the likelihood of producing a word with the lowest and highest closeness centralities. Our results indicated that multiplex closeness centrality was a significant predictor of picture naming performance, where words with high closeness centrality were more likely to be produced than words with low closeness centrality. Additionally, multiplex closeness centrality outperformed single-layer closeness centralities and other multiplex network measures, and remained a significant predictor after controlling for psycholinguistic variables and group differences. Furthermore, we found that the facilitative effect of closeness centrality was similar for both types of aphasia. Our results underline the importance of integrating multiple measures of word similarities in cognitive language networks for better understanding lexical retrieval in aphasia, with an eye towards future clinical applications.