This bit me too. It also doesn't remove it self from the list of daemons, thus running rc.d list shows lighttpd as "STARTED" even though it has crashed. To get it to start you have to remove both /run/lighttpd/lighttpd-angel.pid file and /run/daemon/lighttpd

Couldn't you use the get_pid function that is provided in /etc/rc.d/functions - which simply use pidof - instead of saving the pid to file.
Simply removing the get_pid function at the top of /etc/rc.d/lighttpd seems to work for me, but I can by no stretch say that I have properly tested it. This doesn't however address the issue of autoremoving lighttpd from /run/daemons but this might not even be an issue.

[EDIT]
I misunderstood how the light-angel worked, the patch I submitted doesn't work, please disregard.
Submit a patch here if you're interested.
[EDIT 2]
Something like:

get_pid() {
local pid
local name
pid=$(cat $pid_file 2>> /dev/null)
if [ -n "$pid" ]; then
name=$(ps -p $pid -o comm= 2> /dev/null);
if [ -z "$name" ]; then
rm -f $pid_file
pid=""
fi
else
pid=$(pgrep -f /usr/sbin/lighttpd-angel)
fi
echo $pid
}

probably works. I'm sure there are better way of fixing this and I'm still not certain why it's necessary to store the pid in a file instead of using 'pidof'.