If you can sit through lunch alone without hiding in your phone, you can handle almost anything.

Holding a phone is mostly holding a shield. Sitting alone in a busy room feels like an announcement about you, so the screen gives your eyes somewhere to be and the moment stops feeling public. What is uncomfortable is being seen, not the being alone, and those are worth separating. Once you can sit in a room without cover, a lot of smaller fears lose their grip.

Try five minutes with the phone face down, eating slowly, looking around. Five, not the whole lunch. And if being alone there is not a choice you made, that is a different situation and worth saying to somebody.