Yes, you need to make changes to your name server. Lighttpd is webserver and not dns server. So make IP changes to your dns server. If your lighttpd IP is 22.214.171.124, it should be as follows in BIND:
do i create an A record to point the domain name to my ip address and then have lighttpd resolve it back to my domain name?
yourdomain.com IN A 126.96.36.199
what, exactly, do i have to put in my lighttpd.conf? and is that, in fact, how this whole thing is done
Lighttpd.conf should be as follows:
Replace /home/lighttpd/yourdomain.com/http with actual path.
server.document-root = "/home/lighttpd/yourdomain.com/http"
server.port = 80
server.bind = "188.8.131.52"