Combine the lemon juice, olive oil, garlic, and dried spices in a sealable bag or container. Add the chicken breasts and allow to marinate in the fridge for 1 to 4 hours.
Combine tomatoes, cilantro, parsley, olive oil, balsamic vinegar, celery salt, salt, and pepper in a medium bowl. Cover the bowl and place them in the fridge to marinate for 20 to 30 minutes.
Prepare the sauce by combining the avocado, cilantro, yogurt, lime juice, salt, and pepper in a blender. Blend until smooth. Add water 2 tablespoons at a time until the sauce has a consistency that will allow you to drizzle it. Pour it into a squeeze bottle and store in the fridge until ready to serve.
Preheat the grill to medium-high and grill the chicken breasts for 3 to 6 minutes per side, until it reaches an internal temperature of 165° F.
Place the chicken on a serving platter, drizzle the avocado sauce over it and top with the marinated tomatoes and cheese. Serve immediately.