|Abstract:||Research in Optimality Theoretic syntax tends to focus on language universals and the prediction of systematic language-particular properties by means of constraint interaction, often appealing to the principle of Richness of the Base. However, this has left the role and formal status of the lexicon in such models largely uninvestigated. In this paper we look at some existing architectures for OT syntax, notably the LFG based OT-LFG, and the consequences of these approaches for the syntax-phonology interface, lexical lookup, computational properties of the system and the ability to deal with non-systema tic language particularities. On the basis of this exposition we argue that the lexicon should be modeled as an extra argument of GEN, the universal function from inputs to candidate sets. This setup is able to deal with phenomena that were problematic for other architectures, while still respecting core aspects of Richness of the Base.