Heat grill to high. Brush the cut side of the lobster with oil and season with salt and pepper. Grill, cut-side down until golden brown, and just cooked through. Flip for 45 seconds to just heat through. Remove from the grill and slather with curry butter.
Heat oil in a small saucepan on the grates of the grill or on the side burners. Add onions and garlic, curry powder and wine and cook until reduced, about 30 minutes. Strain. Place the butter in a bowl, add the curry mixture and mix until well combined, season with salt.