Combine all the sauce ingredients in a small bowl. Stir well and set aside.
Bring a pot of water to a boil. Cook the lo mein noodles according to the instructions on the packaging. Rinse with cool water to stop the cooking and set them aside.
Heat the oil in a large nonstick skillet over medium-high heat until hot. Add the garlic, ginger, and green onion and saute until fragrant, about 1 minute.
Turn the heat to high and add the carrots, snow peas, and baby bok choy. Stir fry until the vegetables begin to soften, 1 to 2 minutes.
Add the cooked lo mein and toss with a pair of tongs to distribute the vegetables. Pour the sauce onto the noodles. Cook, tossing continuously, until the liquid is fully absorbed and the noodles are fully coated.