I know you can switch on Tomcat in Plesk, but I think you're better of by installing Lucee with its own Tomcat instance.
So that means not using the Plesk Tomcat at all. Plesk has its own way of doing stuff, and after an update of Plesk, you might find that your configuration is messed up.
For running the sites, that you've setup in Plesk, with CFML you may just add the extra Apache configuration (called "Additional directives for HTTP" under "Web Server settings") per website.
If it would have been Linux you would also need to add lucee to the plesk group that has created the directory of your site (lucee needs write access to create the WEB-INF folder).
This is how I managed to get it running without a problem.