Return wok or skillet to stovetop and reduce heat under pan to medium. Add 1 ½ teaspoons sesame oil and 1 tablespoon avocado oil to pan. Continue heating pan, tilting and swirling as needed, until oils are hot and shimmery.
When oil is hot, add 1 pound boneless, skinless chicken breasts, 3 tablespoons low-sodium soy sauce, 1 tablespoon butter, 2 teaspoons fresh lemon juice, salt (to taste), and freshly cracked black pepper (to taste) to pan.
Stir all ingredients together until well incorporated, then sauté chicken 5 to 7 minutes, stirring only 1 to 2 times, until chicken is browned and no longer pink.
Place second large wok or skillet on stovetop over medium-high heat. Add 1 ½ teaspoons sesame oil and 1 tablespoon avocado oil to pan, then continue heating pan until oil is hot and shimmery.
When oil is hot, add 8-10 ounces zucchini pieces, 2 cups white onion slices, 2 cups quartered baby bella mushrooms, 1 tablespoon butter, 1 tablespoon low-sodium soy sauce, salt (to taste), and freshly cracked black pepper (to taste). Stir until all ingredients are well-incorporated.
Once incorporated, sauté vegetables, stirring occasionally, approximately 6 to 8 minutes or until all vegetables are tender.