> Lean, applied to software, would mean that the software team can see opportunities to improve their process and/or tools, and would have the power to do so.

Yes, that's exactly what Lean in software means (and you'll note that it has a very close relation to Agile principles -- Lean is pretty much Agile with more focus on measurable output and several decades more of development behind it -- both for the good and the bad [there's a lot of depth in the literature of practices and how and when they work to draw from for your circumstances, but there's also breadth and depth in the buzzword snake-oil].)