Place together tomatoes, basil, olive oil, garlic, balsamic, salt and pepper, into a small bowl and toss together. Do this as the grill is warming up.
For the Grilled Romaine:
Preparation: Prepare grill for direct grilling targeting 500 degrees F in the cooking chamber using lump charcoal. Brush both sides of romaine with olive oil, and sprinkle with salt and pepper.
Grill: Grill the romaine hearts on each side until lightly browned on both sides (about 2 minutes each side). While the romaine is grilling place the lemon halves on the grill about 4 minutes (until you see grill marks).
Serve: Remove from heat, and top with the tomato basil mixture and a squeeze of fresh grilled lemon and a drizzle of aged balsamic.
Notes
Important: To avoid wilting the salad the grill grates must be hot. Be sure that the romaine hearts are dry before seasoning them. Water will cause them to steam and wilt versus with olive oil. So they need to be dry.