Prepare the noodles according to the package directions, drain and set aside.
In a small mixing bowl, combine all sauce ingredients and whisk until completely combined.
In a 12-inch skillet over medium-high heat, add 1½ tablespoons of the vegetable oil. Add the cubed chicken breasts and cook for 5 to 7 minutes, until no longer pink inside. Remove the chicken and set it aside.
Keeping the heat on medium-high, add the remaining vegetable oil and the sesame oil. Add the sliced onions and carrots. Sauté for 3 to 4 minutes, stirring constantly.
Add the sliced red peppers, broccoli florets, sugar snap peas, fresh minced garlic, and grated ginger. Reduce the heat to medium, to keep the garlic from burning. Continue to stir constantly and cook for 3 minutes.
Whisk the sauce then pour over the vegetables. Cook for 1 to 2 more minutes until the sauce begins to thicken. Remove the pan from the heat.
Add in the chicken and cooked lo mein noodles. Using tongs, toss to completely coat the chicken and noodles.
Garnish with the sliced green onions and serve while hot.