Remove beards on mussels, and scrub shells well with a brush. Discard open or cracked mussels. Set aside.
Combine 1/4 cup lemon juice and next 5 ingredients in a large bowl; set aside.
Sprinkle mussels with salt, black pepper, and 2 tablespoons lemon juice. Place mussels in a grill basket.
Grill, with lid closed, over high heat (400º to 500º) about 10 minutes or until shells open. Discard any unopened mussels.
Add mussels to lemon mixture; toss well. Drizzle with remaining lemon juice, and sprinkle with parsley. Serve immediately.