Stine - my girlfriend - has tried and tried - it doesn't work with lith!!
at least the FOMa emulsion we use. Suspecting a chemical present in the emulsion that makes the process go way too fast...
however - in the book Silver Gelatine - there's an example of lith made as a lith re-development image...
(You make your image the "normal" way - then bleach away the whole think and redevelop it in lith... that way the end result can't be darker than the original...
we havn't tried it on other brands, so maybe...?
EDIT: Stine has, however had exceptional results in using Lith developer in combination with a normal soft developer for two bath developing. Amazing how many tones one can get this way! (But that's not lith printing - "just" good darkroom work...,-))