Tip:If your gas grill’s heat is controlled front to back, heat on high for 5 minutes, then reduce the heat to medium. Place the clams on half of the grill and cook, covered, for 3 minutes and then place the skillet on other side of grill. Once the butter is melted and the clams begin to open, transfer the clams with tongs to the skillet.
Heat a gas grill or prepare a charcoal grill with one half on medium high, and the other half on medium low.
Put the clams directly on the medium-high-heat side of grill.
Put the butter, wine, garlic, and paprika in a 12- to 14-inch heavy ovenproof skillet and place the pan on the medium-low-heat side of the grill.
Cover the grill and cook the clams, checking occasionally, until they open fully, 6 to 8 minutes. Transfer the clams as they open to the skillet (discard any that do not open after 8 minutes). Carefully remove the skillet from grill. Squeeze the lemon halves over the clams and sprinkle with the parsley.