The phrase "lay out" typically means to organize or arrange something in a particular manner. Synonyms for "lay out" include "arrange," "organize," "prioritize," "plan," "design," "set up," "assemble," "prepare," "layout," and "structure." These synonyms can all be used in similar contexts, such as when describing the process of laying out a document or organizing a workspace. Additionally, synonyms like "map out" or "plot" can be used when describing a more detailed or complex plan or strategy. Overall, there are many ways to express the idea of laying out something in a clear and organized manner, depending on the particular context and level of detail involved.