Remove the salmon from the refrigerator 30 minutes before cooking to bring it to room temperature. This ensures even cooking.
Preheat your grill to medium-high heat (around 375-400°F). Clean and oil the grates well to prevent sticking.
In a small bowl, whisk together lemon juice, olive oil, 2 tablespoons of the chopped dill, garlic, salt, and pepper.
Pat the salmon fillets dry with paper towels and brush both sides with the lemon-dill mixture.
Place the salmon skin-side down on the preheated grill. Top each fillet with a lemon slice.
Grill for 4-5 minutes with the lid closed, until the salmon is golden brown on the bottom.
Carefully flip the fillets and cook for another 3-4 minutes, or until the salmon is cooked to your preferred doneness.
Transfer to a serving plate and sprinkle with the remaining fresh dill.