I have encountered both forms of the idiom new lease of life and new lease on life. Is there an interesting story behind the difference?
Just to set out the usage history - new lease of life was around first, and is still more common...
...but since it's common these days to speak of taking [out] a lease on [something], it's easy to see why increasing numbers of people mishear or misremember the "original", or have only ever heard the revised form anyway.
EDIT: I won't clutter up this answer with two more charts, but if you click on the link above, and toggle the corpus between American and British, you'll see that almost all "new lease on life" usages are American. I have no authoritative source to back me up here, but I believe this kind of minor adjustment to phrasing happens more often in US than UK usage. Probably for several reasons, but in particular I would single out the (to me, still astonishing) fact that for one in five Americans, English is not exactly the "Mother Tongue". Even though I imagine most of those 47M people would say they do in fact speak perfectly good English, it seems to me if you don't grow up in an English-speaking home (or, setting the bar higher, where everyone only speaks English, as did their parents), there's a far greater chance that non-standard usages will catch on if they seem more logical and thus easier to "learn").