Pat the salmon fillets dry with paper towels. Combine the lemon zest, lemon juice, olive oil, garlic, salt, pepper and herbs in a small bowl. Mix well. Remove 2 tablespoons marinade and set aside.
Pour the remaining marinade over the salmon making sure it is coated on both sides. Marinate the salmond in the refrigerator for 1 hour before grilling.
Set all the burners on your gas grill to high. Cover the grill and preheat for 15 minutes. Clean the grates with a grill brush.
While the grill is preheating, slice the remaining 2 lemons in half and brush the cut side lightly with vegetable oil.
Generously and carefully oil the grates of your grill using tongs and folded paper towels soaked in vegetable oil.
Remove the salmon from the marinade and place skin side up on the oiled grill. Add the lemon halves on the grill, cut side down. Leave the grill set on high and close the lid. Grill until the salmon is well charred about 6 to 8 minutes. Remove the lemons when they are charred with nice grill marks.
Using tongs and a large spatula carefully flip the salmon and continue grilling until the center is just translucent, about 1-2 minutes, depending on how thick the salmon fillets are.
Remove the salmon and lemons from the grill and transfer to a platter. Brush the hot salmon fillets with the reserved marinade. Garnish with fresh chopped parsley and serve with grilled lemons on the side.