Thai Larb

Name: Thai Larb
Ingredients: 1/3 cup fresh lime juice; 2 tablespoons fish sauce (such as nam pla or nuoc nam); 2 tablespoons (packed) light brown sugar; 1/2 teaspoon Sriracha sauce; 1 1/2 pounds skinless, boneless chicken breasts, cut into 1-inch pieces; 1/2 cup coarsely chopped shallots; 2 tablespoons thinly sliced lemongrass; 2 kaffir lime leaves, thinly sliced; 1 small red Thai chile, thinly sliced; 1 garlic clove, thinly sliced; 2 teaspoons fish sauce (such as nam pla or nuoc nam); 1 teaspoon kosher salt; 3 tablespoons peanut oil or canola oil, divided; 8 small iceberg lettuce or hearts of romaine leaves; Cilantro tender leaves and stems