Preheat the oven to 425°F. Line a rimmed baking sheet with parchment paper. Toss the sweet potatoes with the olive oil, salt, and pepper. Roast in a single layer until tender and lightly browned, about 25 minutes.
In a medium saucepan, heat the pork with the barbecue sauce and 1 tablespoon water. Spoon onto buns and top with lettuce leaves and tomato slices. Serve with sweet potatoes.