Preheat a grill to medium-high heat. Season the salmon with salt and pepper. Brush the salmon with olive oil and 1 tablespoon of lime juice. Grill for 4 minutes per side, or until cooked through.
In a small bowl, combine the avocado, tomatoes, cilantro, remaining 2 tablespoons of lime juice and a pinch of salt. Serve the salmon topped with the avocado salsa.