A couple thoughts -
I'd also try the Foma emulsion. It's spectacular stuff. A member here uses it for bromoil printing, but I've never tried it in lith. It comes with a hardener, so you'd want to test with and without. I've read so many comments and threads that seem to point to LL having some uniformity problems from batch to batch, but the Foma liquid is just the shizzle. Winderful product.
Biggest issue with lith is the development time - we generally heat the developer up to speed the process. But in my work with foma, I chill all my chemistry (I've only used it on canvas, but it can lift quickly). So you may be in for some really long developing times, or emulsion lifting. Maybe on a rag paper it would be locked on a little better.
The bleach and re-develop takes care of the time issue, but I've never been happy with that. Highlights in lith just don't seem to return, so your first print would possibly need some heavy exposure or flashing. While I like the color shifts in lith, what I love most is the strange ways it can render tonality. it can be otherworldy and very interpretive, and I haven't achieved that with 2nd pass lith.
The most extreme lith colors come from warmtone papers - I don't know how that would work with emulsions, and i's really best on the classic papers, though there's a current Foma that liths very warm.