Lightly dust a large baking sheet with flour. Stretch dough into a large oval on baking sheet. Brush with 1 tablespoon oil. Place dough, oiled side down, on grill grates. Grill, uncovered, until dough starts to puff and grill marks appear on bottom, 2 to 3 minutes. Brush top of dough with 1 tablespoon oil; flip. Working quickly, top dough evenly with lamb, onion, and mozzarella. Close grill and reduce heat to medium. Grill until cheese is melted, about 3 minutes. Remove from grill.