Cook lo mein noodles according to package directions for al dente. Drain and set aside.
While the pasta is cooking, toss the chicken pieces with the salt, pepper, and sesame oil in a large bowl.
Place a deep skillet over medium-high heat and add the prepared chicken to the pan once hot. Cook until the chicken is done, about 3 to 4 minutes.
Add the garlic and ginger in and cook for 1 additional minute, stirring constantly so the garlic and ginger don't burn. Remove the cooked chicken from the pan and set aside.
Add the olive oil and carrots and bell peppers to the pan and cook for 3 minutes. Then add the peas and mushrooms and cook for 2 additional minutes, stirring frequently.
While the veggies are cooking, whisk together the sauce ingredients in a medium bowl. Set aside.
Add the cooked chicken and lo mein to the skillet with the vegetables. Add in the sauce and toss to coat. Cook for an additional 3 to 5 minutes so the sauce thickens slightly and everything is heated through.
Portion into bowls and garnish with green onions if desired.
Notes
Buying tubes of garlic and ginger paste makes prep super easy. If you can't find them in the produce department (or don't want to go that route), you can finely mince fresh garlic and ginger until you have to correct amount.