Make the crispy rice chips:
Heat the oil in a small (6- or 7 inch) skillet over medium-high heat until a small piece of rice wrapper puffs on contact. Fold the rice wrapper in half, then in half again, to create four quarters. Then cut into four pieces along the folded lines. One at a time, drop the rice wrappers into the oil and fry until crisp and puffed, 5 to 10 seconds. Drain on paper towels and season lightly with salt.
Make the spread:
In a small bowl, combine the mayonnaise, 1 tablespoon mustard, 1 teaspoon sesame oil, ½ teaspoon fish sauce, ½ tablespoon ginger, and ½ teaspoon lemongrass. Stir in the scallion greens and chill until ready to use.
Make the burgers:
In a medium bowl combine the lamb and beef with the remaining 1 1/2 tablespoons mustard, 1 1/2 teaspoons fish sauce, 1 tablespoon ginger, 2 ½ teaspoons lemongrass, the shallots, soy sauce, and garlic.
Mix gently with your hands to combine, divide into four equal-sized balls, and press into 5-inch patties. Use your fingers to form a ½-inch deep, 2-inch round dent into the top of each burger (this helps the burgers remain flat when grilling).
Season the burgers on both sides with salt.
Heat a grill or grill pan over medium-high heat. Brush the grill with oil, place the burgers into the grill pan, indented side down, and press gently (you’ll hear some sizzling).
Grill until the underside is charred, 3-4 minutes. Flip and grill until the underside is charred and the burgers are cooked to medium, another 3 to 4 minutes. Remove to a plate and cover with foil to keep warm. Toast the burgers in the grill pan, cut side down, until golden and charred, 1-2 minutes.
Assemble the burgers:
Spread about 1 tablespoon of the mayo mixture on the top and bottom of each bun. Arrange 2 lettuce leaves on the bottom half of each bun, followed by a burger patty and some of the shredded carrots and cucumber. Top each with a few basil and mint leaves, and a rice chip, close the burger with the top half of the bun, and serve immediately with the remaining rice chips.