In a medium bowl, combine the lime juice, 2 tablespoons oil, 1 tablespoon soy sauce, ginger, and garlic. Add the shrimp and let marinate in the refrigerator for 30 minutes.

In a medium skillet, heat the remaining oil over medium-high heat. Add the bell pepper, green onions, and water chestnuts, and cook, stirring constantly, for 3 minutes. Add the shrimp and marinade, and cook until the shrimp are pink, about 3 minutes. Stir in the remaining soy sauce.

Divide the lettuce into leaves. Spoon about one-quarter cup of the mixture down the center of 1 lettuce leaf. Fold the bottom edge and sides up and over the filling. Repeat with the remaining lettuce leaves and shrimp filling.