Oh, I wasn't talking about synchronized lyrics (lyrics that have timestamps), I was talking about the sync/backup function where MusicBee exports/syncs music to another location. Sorry, there's overloaded terminology here.
It's the Sony Walkman ZX-707, and it can read lyrics from .lrc files. In fact, it did do so for a while (both time-synchronized and unsynchronized lyrics), but then stopped for some reason. I was trying to troubleshoot why those lyric files weren't being read anymore and didn't realize at the time that MusicBee won't export lyrics to a storage device (the microSD card) if the music file is already present there.