Heat the oil in a skillet. Add the onion and green onion and cook until soft, about 4 minutes. Add the garlic and cook 30 seconds.
Add the chicken to the pan and cook until browned and almost cooked through, about 3 to 4 minutes. Add the soy sauce and sesame oil. Season with salt and pepper. Cook until chicken is done, about 2 more minutes.
Remove from the heat and add the lemon zest and lemon juice. Garnish with the chopped green onions.