Snap off and discard woody bottoms. On a platter, drizzle asparagus with olive oil and toss with crushed garlic and celery salt.
For a charcoal grill, place asparagus on the rack of an uncovered grill directly over medium coals. Grill for 7 to 10 minutes or until asparagus is crisp-tender, rolling asparagus occasionally to ensure even cooking. (For a gas grill, preheat grill. Reduce heat to medium. Place asparagus on grill rack over heat. Cover and grill as directed:)
To serve, transfer asparagus to a serving dish sprinkle with parsley, lime zest and lime juice; serve!