The cognate facilitation effect, a classic example of cross-language interaction in the bilingual lexicon, has mostly been studied in adults. We examined the extent to which such effects occurred in simultaneous bilingual children’s word processing, to what extent these were modulated by language dominance, and to what extent this differed between comprehension and production tasks. Simultaneous bilingual Dutch-Greek children, ranging from Dutch-dominant to Greek-dominant, performed auditory lexical decision and picture-naming tasks in an online experiment. Cognate facilitation effects emerged in both tasks but manifested themselves differently. In lexical decision, there was an interaction effect with language dominance in accuracy, while in picture naming there was a main effect in reaction times. These findings suggest that, similar to what has been found for adults, simultaneous bilingual children have an integrated lexicon, in which both languages are interactively connected. Effects may differ as a combined result of factors such as comprehension versus production and individual differences in language dominance. Importantly, despite such differences, our results show that cognate effects emerge across tasks and across a range of individual children’s language dominance, indicating that shared representations within the bilingual lexicon are accessed during both word comprehension and production.