Mix 2 tablespoons of the oil, the parsley, lemon zest, lemon juice, garlic, cayenne pepper, and ½ teaspoon salt to form a paste. Reserve 1 teaspoon of the paste for the asparagus and smear the rest on both sides of the steaks. Allow the steaks to stand at room temperature for 15 to 30 minutes before grilling.
Prepare the grill for direct cooking on medium heat (350° to 450°F).
Remove and discard the tough bottom of each asparagus spear by grasping at each end and blending it gently until it snaps at its natural point of tenderness, usually about two-thirds of the way down the spear.
Mix the remaining tablespoon of oil and the reserved 1 teaspoon paste, and then brush the mixture on the asparagus. Season the steaks and asparagus evenly with salt and black pepper.
Grill the steaks over direct medium heat, with the lid closed, until cooked to your desired doneness, 8 to 10 minutes for medium rare, turning once or twice. At the same time, grill the asparagus over direct medium heat until crisp-tender, 6 to 8 minutes, turning occasionally. Remove the steaks and asparagus from the grill and let the steaks rest for 3 to 5 minutes. Serve the steaks warm with the asparagus.