Cold sliced Asian pot roast would be great. Roast chicken is so nice and juicy. Sliced lamb with onion or garlic confit and lettuce would be good on olive bread. You could also put lamb in a pita with grilled eggplant, feta cheese, chopped red onion, and chopped tomato. I'd keep the vegetables separate and assemble them right before eating so the pita doesn't get soggy traveling.
Pasta salads are a pretty popular picnic food.
Speaking of lamb, you could toss bowtie noodles and pieces of lamb loin with some flat parsley, some chopped celery. You could have it plain or with a curry sauce, then you could eat it with some store-bought mango chutney. Some great olives. Or grilled shrimp that was marinated first. If it's marinated and cooked it will keep for a couple of hours.