The goal of the present study was to identify the cognitive processes that underlie lexical ambiguity resolution in a second language (L2). We examined which cognitive factors predict the efficiency in accessing subordinate meanings of L2 homonyms in a sample of highly-proficient, Spanish–English bilinguals. The predictive ability of individual differences in (1) homonym processing in the L1, (2) working memory capacity and (3) sensitivity to cross-language form overlap were examined. In two experiments, participants were presented with cognate and noncognate homonyms as either a prime in a lexical decision task (Experiment 1) or embedded in a sentence (Experiment 2). In both experiments speed and accuracy in accessing subordinate meanings in the L1 was the strongest predictor of speed and accuracy in accessing subordinate meanings in the L2. Sensitivity to cross-language form overlap predicted performance in lexical decision while working memory capacity predicted processing in sentence comprehension.