In a small bowl, whisk together the olive oil, lemon juice, minced garlic, chopped dill, and chopped parsley.
Place the salmon fillet on a plate and coat both sides with the herb marinade, seasoning with sea salt and black pepper.
Preheat your grill or grill pan to medium-high heat and lightly oil the grates to prevent sticking.
Place the salmon on the grill skin-side down and cook for 4-5 minutes until the skin is crispy and releases easily.
Toss the asparagus spears with a tiny splash of water or lemon juice and place them on the grill next to the salmon.
Flip the salmon carefully and grill for another 3-4 minutes, along with the lemon slices, until the fish is opaque and the asparagus is charred.
Remove from heat and serve the salmon topped with the grilled lemon slices and a side of tender asparagus.