The best replacement for litespeed is apache.

The best alternatives to litespeed are rated as following:
★★★★★  apache
★★★  nginx
★★★  moots
★★★  lynskey
★★  lighttpd
★  seven
★  merlin
★  cervelo
★  sql 2008 compression
★  serotta
★  open litespeed
  redgate
  redgate sql backup
  ngnix
  van nicholas
  ross evolution
  colnago

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

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



Google Trends

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