The combination of game birds and green grapes is common in southern France and Italy.
Trim base of endives, remove any darkened outer leaves, and slice in half lengthwise. In a medium saucepan, bring 2 1/2 cups of water to a boil. Add lemon juice, 1 tablespoon sugar, 1/2 teaspoon salt, and endives. Reduce heat; simmer until tender, about 15 minutes.
Rinse squabs, and pat dry. Cut in half. Remove backbones and necks (set aside) and excess fat. Sprinkle with salt and pepper.
Heat oil and 1 teaspoon butter in a large skillet over medium heat. Place squabs, backbones, and necks in skillet. Brown on all sides, starting skin side down, for a total of 10 minutes.
Transfer squabs and bones to a plate. Drain fat from pan, return to heat, and add wine and grape juice. Bring to a boil. Return squabs and bones to pan, reduce heat to medium low, and cook, partially covered, for 12 to 15 minutes.
Heat remaining butter in another skillet over medium heat. Sprinkle endives with remaining 1/2 teaspoon sugar and place, cut side up, in skillet. Cook on both sides until golden brown, about 5 minutes.
Transfer squabs to a plate. Discard bones. Strain cooking liquid, skim fat, and return to skillet. Bring to a boil, and reduce slightly until thick, about 3 minutes. Add squabs and grapes; cook until grapes are heated through. Serve with endives.