Cook the lo mein noodles according to package instructions until al dente. Drain and set aside.
In a small bowl, whisk together soy sauce, oyster sauce, hoisin sauce, sesame oil, chicken broth, cornstarch, and white pepper. Set the sauce mixture aside.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat.
Add the sliced chicken breast to the skillet and cook for 4-5 minutes until fully cooked and lightly browned. Remove the chicken from the skillet and set aside.
Add the remaining 1 tablespoon of vegetable oil to the skillet.
Add the minced garlic and sauté for 30 seconds until fragrant.
Add shredded carrots, sliced bell pepper, and snap peas to the skillet. Stir-fry the vegetables for 3-4 minutes until they are tender-crisp.
Return the cooked chicken to the skillet with the vegetables.
Add the cooked noodles and pour the prepared sauce over the mixture.
Toss everything together gently to evenly coat the noodles, chicken, and vegetables with the sauce. Cook for an additional 2 minutes until heated through and the sauce has thickened.
Remove from heat and stir in the sliced green onions.
Serve immediately.