To be 'lean', literally, is to be lacking in fat: lean people, lean bacon, lean management. The word is Anglo-Saxon and was first used of cattle. It isn't always a good thing - no one likes lean years - but in business it is.
This started in the 1980s, with engineer John Krafcik's phrase 'lean production' to describe the waste-cutting system used by Toyota. Now, a Silicon Valley entrepreneur called Eric Ries is using the term for his Lean Startup movement.
Waste not, want not.