I would also like support for lighttpd. I don't think you have to actually do much except add some rewrite rules to the installation FAQ and a check for lighttpd in one of the PHP files.
http://blog.alexou.net/2012/09/lighttpd-w3-total-cache/
http://webcache.googleusercontent.com/search?q=cache:3gIMPAuhfgQJ:www.hostmasteroftheday.com/2013/02/w3-total-cache-lighttpd-minify (the LUA script would seem to be unnecessary with the proper rewrite rules)