Whisk first 3 ingredients in medium bowl to blend. Mix in next 4 ingredients. Season salsa to taste with salt and pepper. Do ahead: Can be made 8 hours ahead. Cover and chill. Stir shallot, cilantro, jalapeno, garlic, salt, black pepper, paprika, and cumin in large bowl to blend. Add lamb and mix gently to combine. Shape mixture into four 1/2-inch-thick patties. Arrange on small baking sheet. Do ahead: Can be made 8 hours ahead. Cover and chill. Spray grill rack with nonstick spray and prepare barbecue (medium-high heat). Grill buns, cut side down, until golden, about 2 minutes; transfer to work surface. Place lettuce and large spoonful of salsa on each bun bottom. Grill burgers until slightly charred and cooked to desired doneness, about 4 minutes per side for medium-rare. Place 1 burger on each bun. Top each with mayonnaise and bun top. Serve with remaining salsa.