Dave:

I'd be inclined to stick with "Lizzie" (however spelt) as a name pure and simple.  Leeze me, meaning "lief is me" (an endearment of the kind you mention) is the closest thing I can find to your suggestion, and is probably a bit too much of a stretch.  Always best to keep these things simple; when there's an obvious meaning, it's usually the right one!

Malcolm