In large skillet or wok over medium-high heat, warm 1 ½ teaspoons sesame oil and 1 tablespoon neutral oil. Once oils are hot, add chicken pieces. Let chicken cook for 1 minute without stirring.

Add 2 tablespoons soy sauce, 1 tablespoon butter, 2 teaspoons fresh lemon juice, salt, and pepper to skillet. Cook until chicken is no longer pink, approximately 1 to 3 minutes. Stir no more than once or twice so that chicken will brown nicely.

Transfer cooked chicken to medium bowl and set aside. Wipe out skillet (or wok) to use again.

Heat 1 teaspoon neutral oil in skillet over medium-high heat. Add diced onion and frozen vegetables. Sauté until onions are almost translucent, approximately 3 minutes.

Move vegetables to one side of skillet. Crack eggs into skillet and scramble with spatula until cooked through.

Add 4 cups cooked rice and 3 tablespoons butter to skillet. Stir frequently and cook 5 minutes, then stir in 3 tablespoons soy sauce and cook 1 additional minute.

Stir in chicken, salt, and pepper. Cook until everything is well combined and warmed through, then portion into bowls, garnish with sesame seeds if desired, and serve warm.