You need ice packs, not a cooler
You can’t keep perishable food safe for hours without steady cooling, so the best camp lunch box is a soft-sided insulated bag with frozen ice packs, plus a vacuum-insulated food jar for hot meals.
For a day hike, don’t drag a hard cooler. A decent insulated lunch bag (they’re basically small soft coolers) with a couple of frozen ice packs will keep sandwiches, yogurt, cheese, and even that tuna salad safe for 4–6 hours, which covers most trips. Get one with thick insulation and a zipper that seals tight, not a thin tote.
If the weather’s hot or you’re going longer, swap some sandwiches for warm food in a vacuum-insulated food jar. Soups, chili, pasta—these stay hot for hours and don’t need any refrigeration. That’s your real secret weapon when you don’t want to pack ice.
If you mean literally zero ice and no hot food, then there’s no lunch box that will keep perishables safe—you just need to pick foods that don’t spoil: nut butter, whole fruit, dried meats, or hard cheese in a cloth bag.
Your future self will thank you when you’re not suspicious of the egg salad at mile six.
