Are you looking to use File Maker as your database for a Web application? I haven't heard of it being supported on the shared servers, but perhaps you could install it yourself on a Windows VPS or dedicated server. AFAIK it doesn't run on Linux (it does run on OS X, but I don't think Lunarpages offers any OS X servers).
If no one from Support chimes in with a more definitive answer, I would email to firstname.lastname@example.org
and ask directly.
Note that from what little I've read about File Maker, it doesn't sound like a very powerful database system. It sounds more along the lines of MS Access than MySQL or Oracle. I would suggest that you not restrict yourself to using File Maker simply because you're familiar with it -- if you want to have a real website you may need to use a real database.