UX is short for User eXperience, and was coined as a term used primarily in software development, meaning…uhmm…user experience. Or, to be clear, that which a user of software experiences during use (as opposed to whatever experience might be presupposed of the user). From what I can see, “UX” has become a specialty of sorts, perhaps akin to “screenwriting,” in which the UX Designer makes design decisions that dictate the course of this or that usage scenario. It appears to have become a sub-discipline of software engineering.
And on that note, as Ivan already alluded, “Lean” is an Engineering term that originated in Manufacturing, but carries varied connotations across different forms of Engineering with regard to “process.” Specifically in software development, it has come about as a re-think of a previously established approach. In that approach, development was accompanied in parallel by the practice of “documentation.” By comparison, the documentation element constituted the majority of time consumed by the process overall. When it came time for trials and testing, it wasn’t uncommon for all that documentation work to become time wasted, as revisions and the findings of testing often required the documentation to be rewritten, if not scrapped altogether. In the quest for “leaner” process, the newer approach is to forego documentation in the early stages, and go right to testing. As testing feedback materializes, changes can be made “on the fly” without getting bogged down in the “fat” of documentation, which is now saved for a later stage of development, when the product is much closer to finalized.