Add the crab and toss with the salt and pepper.
Preheat the grill to high, carefully place all the marinated crab onto the grill, allowing the oil to drip off before putting onto the grill, and cover with lid. Allow to cook about 4 to 5 minutes then turn over and allow to cook another 3 to 4 minutes.
Remove from the grill, and place into a large metal bowl. Squeeze the fresh lemon juice over the crab and toss well.
Serve on a large platter with fresh lemon wedges and chopped Italian parsley.