How to delete lyrics on one layout only ?

You don’t. Stave content is unique to the player (or instrument), rather than unique to the individual layout.

The easiest way would be to copy and paste to a separate player or pair of players, but of course if your source material changes in future you’ll need to update it in two places rather than one. The alternative is to have a separate player or players that you cue into, and then you fudge your cues in such a way that they look like regular notation. I’ve explained how to do this before on this forum, so I’ll leave you to search if that method suits you.