Lighttpd has similar features, but whoever told you the config files are directly compatible was smoking something. You cannot use
.htaccess files with lighttpd.
The config files are totally different, and while fastcgi works similarly once you have it working, you CANNOT just drop apache configs into lighttpd and expect them to work.
Pragmatically, you can expect the default set of lighttpd modules to be installed. If you're allowed to directly edit your site conf files, you can explicitly load any module you need there using this syntax:
server.modules += ( "mod_access", "mod_rewrite" )
In general, you should read through the lighttpd config docs, paying special attention to the section on migrating from apache.
If the lighttpd server has the status module loaded, you may be able to see which modules are loaded there, if you have access to that url. The thing is, the actual loaded modules DO NOT MATTER AT ALL to you if you don't have access to change the config files. There is nothing you can do with a loaded module if you can't configure your site.