Bring a large pot of water to boil. Once the water reaches a rolling boil, add in the lo mein noodles and cook for 3-4 minutes, or according to package instructions.While you wait for the water to boil, prepare your sauce:In a small bowl combine the lime juice, brown sugar, soy sauce, sriracha, ginger, and 1 teaspoon of the sesame oil; whisk well to combine. Set aside until needed.Melt the butter in a large non-stick skillet over medium heat. Add in the crushed red pepper flakes, then pour in the beaten eggs. Stir gently and cook for about 3 minutes. Once the egg is done cooking, keep the pan on the burner but transfer eggs to a small plate; set aside.Add 1 tablespoon of the sesame oil to the pan and increase the heat to medium-high. Add in shrimp and cook for 1 to 2 minutes on each side, or just until firm and pink. Remove shrimp with a slotted spoon and transfer to a clean plate; set aside. Add the broccoli and red pepper strips to the pan, increase heat to high, and add in the remaining sesame oil; stir fry until just charred; about 3-4 minutes. Stir in garlic and cook for one minute, or until fragrant.Add drained noodles to the skillet along with the cooked egg, shrimp, and prepared sauce. Reduce the heat to medium-low, and stir well, making sure all ingredients are coated with the sauce. Cook for a minute or so, just to ensure all ingredients have been warmed. Serve at once.