Combine the butter ingredients. Set aside.
Whisk the marinade ingredients. Reserve and set aside one-half of the marinade to use for basting the lamb on the grill. Pour the remaining marinade into a large, resealable plastic bag. Place the lamb inside the bag, press the air out, and seal tightly. Turn the bag to distribute the marinade, place in a bowl, and refrigerate for 2 to 4 hours, turning occasionally. Remove the lamb from the bag and discard the marinade. Allow the lamb to stand at room temperature for 15 to 30 minutes before grilling.
Prepare the grill for direct and indirect cooking over medium heat (350° to 450°F).
Grill the lamb, fat side down, over direct medium heat, with the lid closed, until nicely marked, 10 to 12 minutes. Turn the lamb over and grill for 5 minutes more, basting the lamb with the reserved marinade. Then move the lamb over indirect medium heat and grill, fat side up, with the lid closed, until an instant-read thermometer inserted into the thickest part of the lamb registers 125° to 130°F for medium rare, 20 to 30 minutes more, basting occasionally with the reserved marinade. Remove from the grill and let rest for 5 to 10 minutes.
Cut the lamb across the grain into thin slices. Melt the herb butter, and then drizzle it over the lamb. Serve right away.