Are the playlists regular playlists or smartlists?
Transferring smartlists are somewhat easy. This can probably be done just by creating a library back-up and restoring it on the Id. Another method is to export the smartlists, transfer them to the Id, and then import them. It's easier because smartlists rely on tags.
Regular playlists are much more complicated. The problem is regular playlists rely on paths to the music file. When things get moved around, those paths change. So, transferring a playlists would require updating all the paths in the playlist.
The best way that I know of is to export a playlist and make sure 'Store paths relative to exported playlist' is checked. Then, as long as the playlist is store in the same directory relative to the music files, and the music files use the same directory structure, it should still work. You might also need to export the playlist as an MPL playlist because Windows and Linux use different file path separators, but I believe MPLs can translate between the two.
There might be some people on the Linux board of the forum that know better ways to do this, but it's not something I've done much.