There are many webservers that allow running lua scripts. The top 2 that come to mind are Apache and NginX. However they don't allow the execution of lua scripts by default, on Apache you need to configure it using a --enable-lua flag and then enable the mod_lua module. You can find more about it here:
http://modlua.org. And for NginX there's an extension called OpenResty (
http://openresty.org/). There's also a webserver in lua called Xavante (
http://keplerproject.github.io/xavante/). As for running then on your host service, I guess you would need to contact them!
Cheers,
Etiene.