In a shallow dish, rub the sea bass with lemon juice and 1 tablespoon, each, of olive oil. Season with salt and pepper and let sit at room temperature for about 20 minutes. This will really allow the simple flavors of the lemon to enter the fish and make it truly fantastic.
Heat a large skillet under medium high heat.
In a medium bowl, combine the tomatoes, onions, basil, dill, and pepper. Add 2 tablespoons of olive oil and mix well. Add remaining tablespoon of lemon juice and give it a quick toss. Add mixture to hot skillet and saute until onions and tomatoes start to soften, about 5-7 minutes. Season with salt and pepper and set aside.
Wipe down skillet and return to heat. Add 1 tablespoon of olive oil and heat until shimmering.
With a paper towel, pat dry the fillets and add to skillet, skin side down. Cook under medium high to high heat until skin is browned, about 4 minutes. Turn and cook until fish is white throughout, about another 4 minutes.
Transfer the fish to plates and immediately top with tomato mixture and a nice piece of crunchy bread.