Eating lunch alone is a seating arrangement, not a verdict on who you are.

A table is not a judgement. Where you sit gets decided by timetables, who had a different lesson, who arrived first, and almost never by anybody’s opinion of you. The story you add is the part that hurts rather than the lunch itself. Plenty of people eating alone today will be in company tomorrow.

If it happens, give the twenty minutes something to do: a book, a plan for the evening, a message to somebody. On another day, ask one person to sit with you, since that is how most of this changes. And if somebody else is alone, there is a spare seat in front of you.