Hi
I had the same boring problem.
Pi-hole was running good (for some months) and after a update no more web-interface was aviable.
I followed the insctructions on Lighttpd does not start - #11 by djcraysey but this didn't solved the problem.
But the Idea was good: Installing a program that contains lighttpd.
So I found a workaround:
sudo apt-get install gamin (this re-installs lighttpd)
sudo apt-get purge gamin (this uninstalls lighttpd)
curl -sSL https://install.pi-hole.net | bash (this re-installs lighttpd for the pi-hole).
For me it worked, I hope it will help you too.