In a medium bowl, add the chicken, half of the lemon juice, half of the Italian seasoning, half of the olive oil, salt, and pepper. Toss to coat and cover or store in a Ziploc bag. Refrigerate the chicken mixture for at least 30 minutes or overnight.
When ready to cook, remove the chicken from the marinade, letting excess drip off. Heat a large skillet over medium-high heat. Add the chicken in a single layer. Cook for 8-12 minutes (depending on thickness), until chicken is just cooked through. Remove from pan and set aside. It will continue to cook as it sits, so make sure not to overcook the chicken.
Add the remaining olive oil to the pan. Then add the asparagus, zucchini, remaining Italian seasoning, and remaining lemon juice. Season with salt and pepper. Cook for 5-7 minutes, stirring occasionally.
Add in the tomatoes, garlic, and balsamic vinegar. Cook for another 2-3 minutes or until all vegetables are cooked through and the sauce has thickened up. Remove from heat and stir chicken back into the pan, toss until evenly coated in the sauce.