Place the pineapple on its side and cut off about 1/2 inch from the top and the bottom. Stand the pineapple upright and cut lengthwise to remove the tough outer skin. After the skin has been removed, shave off any remaining hard bits of peel. Cut the pineapple in quarters, lengthwise, through the core. Lay each quarter flat, and slicing at an angle, remove the hard center core. Cut each quarter in half lengthwise again, rendering 8 long slender pieces of pineapple.
Prepare grill for medium heat direct cooking.
Melt butter in a medium sized sauté pan. Stir in the sugar and cook just until the sugar begins to dissolve. Using about one quarter of this mixture, lightly brush the surfaces of the pineapple. Grill for 8-10 minutes, turning once.
Place the sweetened condensed milk and the pineapple chunks in a blender and puree until very smooth. Pass the mixture through a fine mesh strainer, pressing firmly. Discard the remaining pulp. Stir the milk and lemon juice into the pineapple puree and chill for 30 minutes.
freeze the sherbet following the manufacturer’s directions of your ice cream maker. Place it in an airtight container and cover. Freeze at least one hour before serving.
Yield: 1 quart