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

Add 2 tablespoons soy sauce, 1 tablespoon butter, 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.

Transfer cooked chicken to a 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 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.