Preheat the oven to 375 degrees F (190 degrees C). Lightly grease a 2-quart or 8x8-inch baking dish.
Reserve 1 tablespoon green onions for garnish. Combine the remaining onions with cream cheese, Monterey Jack cheese, Sriracha, soy sauce, lemon zest, and lemon juice and stir until well blended. Fold in crabmeat and pour mixture into the prepared baking dish.
Bake in the preheated oven until bubbly, about 20 minutes. Let stand for 5 to 10 minutes before serving. Drizzle with sweet chili sauce and sprinkle with reserved green onions and sesame seeds, if desired.
While dip bakes, heat oil in a medium saucepan to 350 degrees F (175 degrees C).
Fry 5 to 6 pieces of wonton at a time in batches, flipping several times throughout, until golden, bubbly, and crisp, about 30 seconds. Drain on paper towels and sprinkle immediately with salt. Repeat with remaining wontons and serve immediately with dip. (Alternatively, these chips could be made the day before, cooled completely, and stored in airtight containers).
