Cook lo mein noodles according to package directions until just tender. Drain and set aside.
Heat oil in a large pan or wok over medium-high heat.
Add sliced chicken and cook until lightly golden and fully cooked. Remove from pan and set aside.
In the same pan, add cabbage and carrots. Stir-fry for 2–3 minutes until slightly softened.
In a small bowl, mix soy sauce, oyster sauce, hoisin sauce, sesame oil, sugar, and broth.
Pour sauce into the pan and bring to a gentle simmer.
Add cooked noodles and chicken back to the pan. Toss everything together until well coated and heated through.
Finish with green onions and serve hot.