1. He is delivering lunches to elderly people.

2. He is delivering lunch boxes to elderly people.

3. He is delivering lunch boxes for elderly people.

(Does "lunches" mean "lunch boxes"?
Can we use 'for' instead of 'to'? Do they have the same meaning?)

Lunch boxes is more exact. If he's delivering lunches, he could be delivering bags of food or trays of food.

All of the sentences are correct. In my opinion, "to" is the better preposition.