The best replacement for lighttpd is nginx.

The best alternatives to lighttpd are rated as following:
★★★★★  nginx
★★★★★  apache
★★  apache raspberry pi
★★  cherokee
★★  nginx php
★  litespeed
★  apache2
★  thttpd
  uhttpd
  httpd
  ngix

Your alternative for lighttpd is not listed? Suggest!
Speaking about lighttpd, one probably shouldn't forget about fastcgi.

Other search terms related to lighttpd and their ratings are:
★★★★★ fastcgi
★★★ php5
You have in mind a companion for lighttpd and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of lighttpd in all years. Click on graph for more.
lighttpd
nginx
apache