I think copy and paste should work pretty well, unless the rhythmic structures differ a lot.
Copying the lyrics will put them at the same rhythmic positions, regardless wether there are notes or not. You can shift individual syllables by the current value of the rhythmic grid with Alt+left/right arrow if you need to make small corrections.
Edit: And just in case you’re not aware of it – Edit > Filters > Lyrics can save you much time here. 