Preheat barbecue for medium-high heat and lightly oil the grate.
Place the chicken breast halves between two sheets of heavy plastic (resealable freezer bags work well) on a solid, level surface. Firmly pound the chicken with the smooth side of a meat mallet to a thickness of about 1cm. Brush each chicken breast with olive oil and sprinkle with a pinch of garlic salt.
Cook the chicken breasts on the preheated barbecue until the meat is no longer pink inside and the chicken has good grill marks, 5 to 8 minutes per side. Move chicken to a cooler part of the barbecue to keep warm.
While the chicken is cooking mix together the tomatoes, basil, spring onions, garlic, salt, black pepper and lemon juice in a bowl.
Place a square of aluminum foil onto the barbecue and move a cooked chicken breast onto the foil. Top the chicken breast with about 1/4 cup of the tomato mixture and sprinkle the topping with about 2 teaspoons of Parmesan cheese. Repeat for the other pieces of chicken.
Close the lid on the barbcue and cook the chicken breasts until the topping is hot, 2 to 3 more minutes.