Heat a grill pan or skillet to high heat. In a large bowl mix the onions and 1 tablespoon coconut oil. Place onions in pan and cook for 5 minutes on each side, until both sides are lightly charred.
In a large bowl, add the onion, olive oil, salt and pepper, tomatoes, avocados, basil and lime juice. Toss vegetables and set aside.
Rub fish with the remaining coconut oil and salt and pepper. Place on hot grill pan or skillet and cook for 5 minutes on each side, until fish flakes easily with a fork.