Why do you want to do this? Having a separate server to handle static content, isn't necessarily a bad idea. However, running lighttpd (or anything else) and apache on the same machine seem to be a bit misguided.
If you're having proformance issues, I'd find out where they are coming from. If it's anything like disk IO, memory issues, network issues, etc. running lighttpd isn't going to help. All those issues will still be there (assuming it's ran on the same machine).
If you're problem is long running scripts or similar, maybe it will help a tad bit, but I don't think it would be worth the effort.
In my opinion, if your site needs static content served different then dynamic, then you probably should move that content to another server. It's probably time to start looking at a bigger hosting package.
That being said, I would suggest storing the static content on another disk (on another controller if possible) just to mitigate the lighttpd and apache processes from fighting for disk access. Also, if you have the ram, it's possible to put that static content into a ramdisk for even faster access. Though at somepoint simple network bandwidth limitations are going to come into play.