If I remember correctly, litespeed is not for free for commercial use, and the open litespeed doesn't read apache configurations automatically.
There is also caddy webserver,
https://caddyserver.com/, it seems to be the new cool toy on the block for the last 2 months, it supports both http2 and auto ssl generating and signing through letsencrypt
@mir, I'll pm you few websites behind cloudflare if you still wanna test http2