I saw the note in the readme about contacting the author if I am interested in having it work with lighttpd, so here I am...
I tried a couple of the solutions posted around the internet, mostly the ones that involve tricking w3tc into thinking that it is running on nginx, and had some success with that, in terms of getting the "disk: enhanced" stuff working properly (though the error messages appeared at the top of every admin page, so perhaps it is not working perfectly).
I use dbcache and supercache, and mostly do pretty well, but if the blog has a giveaway, and gets a couple thousand comments, things start to drag, and I was hoping w3tc would be able to help out with that.
But, I think perhaps what I really want is a plugin that automatically puts the site in lockdown mode if the cpu load goes above a certain threshold... that plugin doesn't seem to exist, so maybe I'll have to write my own.
But, anyway, if w3tc supported lighttpd, I'd take another look at it.