Combine soy sauce, lemon juice, ginger, and garlic in a large glass bowl. Add cubed chicken, cover, and refrigerate for 30 minutes.

Heat oil in a large skillet over medium heat. Use a slotted spoon to add just chicken to the skillet, reserving marinade in the bowl. Cook until chicken is no longer pink in the middle and juices run clear, about 5 minutes. Transfer chicken to a plate.

Add green onions and bell pepper to the hot skillet. Cook over medium-high heat for 1 to 2 minutes. Return chicken to the skillet.

Stir cornstarch into the bowl with the reserved marinade. Pour into skillet with chicken and vegetables and increase heat to high. Cook, stirring constantly, until sauce thickens, about 5 minutes.