I'm very late getting into this thread, but
someone needs to mention some of the older Batman crossovers on the Archive:
- Barb's Variations on a Theme trilogy
- SkipD's Luthor's Legacy. It has a prequel, Brothers, but with no Batman
- My own Lois and Clark and Silver and Bruce
All good (well, I'll let you make up your own mind about my story, but I can recommend the others).
FWIW, I can also recommend
Cat-Tales, which I love, but the author is a bit stereotypical Bat-fan in her attitude to Superman, and it should be remembered that CT is based on the comics and
not on L&C.