In a medium bowl whisk the marinade ingredients. Place the steaks in a large, resealable plastic bag and pour in the marinade. Press the air out of the bag and seal tightly. Turn the bag to distribute the marinade, place on a plate, and refrigerate for 2 to 24 hours, turning occasionally.
In a small bowl blend the butter ingredients, including ½ teaspoon salt. Transfer the mixture to a sheet of plastic wrap and roll into a log about 1-½ inches thick. Refrigerate until firm, 45 minutes to 1 hour.
Allow the steaks to stand at room temperature for 15 to 30 minutes before grilling.
Prepare the grill for direct cooking over high heat (450° to 550°F).
Remove the steaks from the bag and wipe off the excess marinade with your hands, leaving a thin coating. Season the steaks evenly with 1 teaspoon salt.
Brush the cooking grates clean. Grill the steaks over direct high heat, with the lid closed as much as possible, until cooked to your desired doneness, 6 to 8 minutes for medium rare, turning once (if flare-ups occur, move the steaks temporarily over indirect heat). Remove from the grill, top with some of the lemon-pepper butter, and let rest for 3 to 5 minutes. Serve warm.