Which should you choose?
Agile UX and Lean UX are two approaches to the modified design processes that fit the way clients and consumers expect modern products and services to be delivered. The terms are typically taken to mean the same thing.
However, the different results that are arrived at from the different methods are clear: Agile UX produces a more polished product; Lean UX produces multiple products of increasing polish. Ultimately, both techniques can arrive in the same place, but via very different routes.