If you run a very busy lighttpd you may get the following:

(network_linux_sendfile.c.143) open failed: Too many open files
(connections.c.606) connection closed: write failed on fd 588
(network_linux_sendfile.c.143) open failed: Too many open files
(connections.c.606) connection closed: write failed on fd 782
(network_linux_sendfile.c.143) open failed: Too many open files
(connections.c.606) connection closed: write failed on fd 782
(network_linux_sendfile.c.143) open failed: Too many open files
(connections.c.606) connection closed: write failed on fd 782

You should increase the file descriptors that lighttpd can used (put into the lighttpd.conf):

server.max-fds = 8192

You may also want to increase the max-workers (also goes into the lighttpd.conf):
http://redmine.lighttpd.net/wiki/lighttpd/Docs%3AMultiProcessor

server.max-worker = 8

This is going to make 8 threads, so depending on your exact setup you may wish to increase or decrease the value.