If you want to host more than one site in Lucee, you’ll need to mimic the mod_cfml headers in your Litespeed server and make sure you have the Mod CFML Tomcat valve installed on the Lucee side.
If your goal is just the simplest server setup possible, have you considered CommandBox? It has the web server built in for you (based on JBoss Undertow) and you can activate ModCFML as a built in feature and spoof the headers all within your server.json file. It does have a few limitations currently, such as if you need different SSL certs per host, etc.
Also, I moved this to a new topic.