I'm not a foobar2000 user, but after some searches, there are Lyrics Show Panel 3 (mostly dead?) and its opensource alternative foo_openlyrics (https://github.com/jacquesh/foo_openlyrics).
Adding LRCLIB source should be easy and straightforward enough (https://github.com/jacquesh/foo_openlyrics/tree/master/src/s...). I'm not very experienced in C++ though, so I suggest opening an issue first to see if the author or anyone are willing to do the intergration.
