Preheat your grill to a medium-high setting.
Brush the salmon fillets on both sides with olive oil.
Season them with salt, pepper, and Italian seasoning.
Slice the lemons and place half of them directly on the grill.
Lay the salmon fillets, skin side down, on top of the lemon slices.
Grill the salmon for about 6-8 minutes.
Flip the fillets and grill for another 2-4 minutes until cooked through.
In a small saucepan, melt the unsalted butter over low heat.
Add minced garlic and chopped parsley, stirring until combined.
Drizzle the garlic herb butter over the grilled salmon before serving.
The lemon slices can be used as a garnish.