Lightly brush four 1-inch-thick wedges of watermelon with vegetable oil on both sides. Grill over medium-high heat until well marked, 2 to 3 minutes per side. Let cool slightly, then cut into small chunks, discarding the rind. Whisk 2 tablespoons lime juice with 2 teaspoons each brown sugar and fish sauce; toss with the watermelon and let stand 20 minutes. Serve in Bibb lettuce leaves with sliced cucumbers, scallions, cilantro and chopped peanuts.