Heat the vegetable oil in a large skillet or wok over medium-high heat.
Add the chicken pieces and season with salt and pepper. Cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the bell pepper, broccoli, and snap peas. Stir-fry for about 3-4 minutes until the vegetables are tender-crisp.
Add the garlic and ginger, cooking for an additional minute until fragrant.
Return the chicken to the skillet.
In a small bowl, whisk together the soy sauce, honey, and lemon juice. Pour the sauce over the chicken and vegetables, stirring to coat everything evenly.
Add the cornstarch mixture to the skillet and stir until the sauce thickens, about 1-2 minutes.
Remove from heat and serve the sticky lemon chicken stir-fry over cooked rice or noodles.