The lexicons of human languages organize their units at two distinct levels. At a first combinatorial level, meaningless forms (typically referred to as phonemes) are combined into meaningful units (typically referred to as morphemes). Thanks to this, many morphemes can be obtained by relatively simple combinations of a small number of phonemes. At a second compositional level of the lexicon, morphemes are composed into larger lexical units, the meaning of which is related to the individual meanings of the composing morphemes. This duality of patterning is not a necessity for lexicons and the question remains wide open regarding how a population of individuals is able to bootstrap such a structure and the evolutionary advantages of its emergence. Here we address this question in the framework of a multi-agents model, where a population of individuals plays simple naming games in a conceptual environment modeled as a graph. We demonstrate that errors in communication conditions for the emergence of duality of patterning, that can thus be explained in a pure cultural way. Compositional lexicons turn out to be faster to lead to successful communication thanpurely combinatorial lexicons, suggesting that meaning played a crucial role in the evolution of language.