In a small mixing bowl, combine the low sodium chicken broth, lemon zest, lemon juice, low sodium soy sauce, sesame oil, garlic, and arrowroot starch. Mix vigorously until no clumps remain. Set sauce aside until ready to use.
Heat large skillet over high heat and add the olive oil.
Add the chicken and cook for 4-6 minutes, or until it starts to cook through. Add the zucchini and mushrooms into the skillet toss everything to coat in the hot oil. Cook for 4-5 more minutes, or until the zucchini starts to soften and the chicken is cooked through.
Add the sauce and cook for one more minute to thicken.