Pat the salmon fillets dry with paper towels and brush them lightly with olive oil. Season generously with salt and pepper on both sides.
Trim the tough ends off the asparagus and rinse them under cold water. Pat dry and brush with a little olive oil, then season with salt and pepper.
Heat the grill to medium-high heat until hot and slightly smoky. Place the salmon fillets skin side down on the grill, hearing a satisfying sizzle.
Lay the asparagus spears in a single layer on the grill, alongside the salmon. Grill the asparagus for about 4-6 minutes, turning occasionally, until they develop some charring and are tender yet crisp.
Check the salmon after about 4-5 minutes; it should develop a golden, crispy skin and the flesh should turn opaque and flaky. Carefully flip the fillets and cook for another 2-3 minutes until done.
Place lemon slices on the grill during the last minute to add a smoky, caramelized flavor. Remove the salmon, asparagus, and lemon from the grill once they reach the desired doneness.
Transfer the salmon to a serving plate, arrange the grilled asparagus alongside, and squeeze fresh lemon over everything for brightness. Garnish with chopped herbs for a fresh touch.
Serve immediately to enjoy the crispy skin, tender fish, and smoky, crisp asparagus with a hint of citrus and herbs.