Hello, Patricia. Everything matters with the bleach and lith redevelop, but yes there are too many variables to reproduce results consistently.
In general, if a normally processed print is to be bleached and redeveloped in lith, it is best that it is slightly "overdeveloped", or a little darker to begin with, and 1/2 to 1 grade less contrast than would normally be desired. You won't notice the loss of density in the blacks as much as in the highlights, as you will always lose some.
Have three or four identical prints going in, and be prepared to lose a couple.
There are examples in the Book of Lith of this process where the printer used Dektol initially, and they are gorgeous so obviously it works. Just speculating, but I don't think the initial developer is not nearly as important as the emulsion you are working with, and would stick with warm-toned lithable papers.
Also, you can achieve something of a solarizing effect if you flash the print while it is redeveloping. An on-camera flash will work. Not a real strong effect, but it's there.