Cook lo mein noodles according to their package directions, then drain thoroughly. Whisk soy sauce, oyster sauce, sesame oil, sugar, water and cornstarch in a small bowl.
Heat 2 teaspoons neutral oil in a large wok or deep skillet over medium-high heat. Stir-fry chicken for 4 to 6 minutes until the thickest strips reach 165°F; transfer to a plate.
Add remaining oil, cabbage, carrot and snow peas and stir-fry for 3 to 4 minutes until crisp-tender. Add garlic and ginger for 30 seconds.
Return chicken, add drained noodles and stir the sauce once more before pouring it around the pan. Toss for 1 to 2 minutes until the sauce lightly coats everything.
Lift and turn the noodles once more to distribute chicken and vegetables evenly, then serve immediately.