Is lighttpd recommended for a production webserver?
Solution 1:
Several large-volume websites use lighttpd, so in that sense it's 'proven' enough. That said, development and/or community involvement has slowed down greatly after the original developer Jan Kneschke landed a job at MySQL working on other things.
The current favorite in the low-resource-requirements & high-speed HTTP server space is nginx (pronounced EngineX). Have a look at the recent stats (second illustration) -- nginx is a late entry on the charts, but it is growing fast and already well ahead of lighttpd in marketshare.
If nginx works for your needs, then I would suggest to use it instead of lighttpd; nginx is benefiting from more active development and more widespread use now (nginx 7.57% versus lighttpd 0.69% of top sites in the above linked Netcraft results).
Solution 2:
There is ongoing development: http://redmine.lighttpd.net/repositories/show/lighttpd
There are also a lot of people using it. There has been some decline though, because nginx is much more hyped. There are also other smaller web servers which are similar to lighttpd, like Cherokee. I used each of them for a while, though just for personal use.
All these servers host serious web sites. You can find them on their wikis, etc. So yes, they are production ready. IIRC YouTube or a similar web site has been using a lighttpd setup for quite a while. Oh, The Pirate Bay is also a prominent lighttpd user.