Rinse steaks thoroughly in cold water; drain and pat dry. Place steaks in a wire grilling basket. Combine butter, lemon juice, salt, and pepper; stir well.
Grill steaks over medium coals 10 minutes on each side or until fish flakes easily when tested with a fork. Baste often with butter mixture, reserving a small amount for sauce.
Add dill to remaining butter mixture; stir well. Serve steaks with dill-butter sauce.