In a small bowl, combine the oil, half of the lemon juice, 1 tsp salt, 1/4 tsp pepper, 1/4 tsp Italian seasoning and whisk to combine. Transfer to a large resealable bag. Add chicken to the bag, seal and refrigerate for 30 minutes.
Heat grill over medium-high heat, then add chicken, discarding excess marinade. Grill until charred and cooked to an internal temperature of 165, about 5-7 minutes per side.
Meanwhile, combine tomatoes, garlic, basil, and remaining lemon juice and season with salt and pepper. While chicken is still on the grill, top each breast with 1 slice of mozzarella and cover until cheese is melted, 2-3 minutes. Top chicken with tomato mixture and serve.