Here's my definition

Lean User Experience is a cross-functional, principle-driven process characterized by rituals that predispose teams to high-quality, high-velocity user experience outcomes.

I also think it's possible that 

Customer Development is the solution to Agile UX process problems. 

Lots to unpack in those two statements. I've been working on that with a workgroup, some of whom will likely be publishing here, since September. I'm heading to the Agile UX retreat in December, and teaching a methods workshop (which we're calling LUXi) this weekend. All this in an attempt to bring together the ideas that are driving innovation with the ideas that have driven great user centered design. UCD, AGILE, and LEAN are each important ideas that, when combined, have the potential to shift how we work and think. We're on the precipice of something profound.