A book at a lunch table for one isn’t hiding. It’s having the best conversation in the room.

Sitting alone at lunch gets read as a failure to be chosen, which is why people arrange their faces so carefully while doing it. A book changes what is happening at that table, though not in the way people assume. You are not covering a gap, you are choosing who to listen to for half an hour.

Try one lunch like that without apologising for it in your posture. No glancing around to check who noticed, since mostly nobody did. Pick something you actually want to read rather than something that looks respectable.