Wash and dry all fruit thoroughly. Combine the mixed berries, cubed melon, and grapes in a large bowl. Portion the fruit salad evenly into 4 lidded containers and refrigerate until packing.
Open the hoagie rolls. Spread 1 tablespoon of mayonnaise on the inside halves of each roll.
Place 2 slices of cheese on the bottom half of each roll to act as a barrier against moisture from the vegetables.
Fold 4 ounces of the sliced beef deli meat onto the cheese layer of each sandwich.
Top the meat evenly with the sliced tomato and lettuce leaves. Close the sandwiches tightly.
Wrap each sandwich firmly in parchment paper or aluminum foil. Store in a cooler with ice packs alongside the fruit cups and serve with potato chips.