Start by boiling a large pot of water. Once boiling, add the lo mein noodles and cook according to the package instructions until tender. Drain and set aside.
In a small bowl, whisk together the lime juice, light brown sugar, soy sauce, Sriracha hot sauce, and fresh grated ginger. Set this flavorful sauce aside for later use.
In a large skillet or wok, heat 2 tablespoons of sesame oil and the unsalted butter over medium-high heat. Once hot, add the minced garlic and crushed red pepper flakes, sautéing for about 30 seconds until fragrant.
Add the peeled shrimp, frozen broccoli florets, and frozen red bell pepper strips to the skillet. Stir-fry for about 3-4 minutes, or until the shrimp turn pink and the vegetables are heated through.
Push the shrimp and vegetables to one side of the skillet. Pour the beaten eggs into the other side and scramble them until fully cooked, about 1-2 minutes.
Add the cooked lo mein noodles and the prepared sauce to the skillet. Gently toss everything together until the noodles are evenly coated and heated through. Drizzle with the remaining teaspoon of sesame oil for extra flavor.
Before serving, taste the dish and adjust the seasoning if necessary. You might find you need a touch of salt, but remember that the soy sauce adds a significant amount of sodium.