In a large saucepan combine granulated sugar and cornstarch; stir in cherries. Cook and stir over medium heat until thickened and bubbly. Remove from heat and stir in almond extract.
In a small bowl beat together cream cheese, brown sugar, and lemon juice with an electric mixer on low to medium speed until smooth.
Spoon about half of the fruit mixture into a 2-quart disposable foil pan. Dollop cream cheese mixture over fruit mixture in the foil pan. Spoon remaining fruit mixture over the cream cheese mixture. Cover pan tightly with foil.
For a charcoal grill, arrange medium-hot coals around edge of grill. Test for medium heat over center of grill. Place foil pan on rack in the center of grill. Cover; grill for 15 minutes. Uncover pan. Sprinkle top of fruit mixture with cake pieces and drizzle with butter. Keep pan uncovered. Cover grill; grill for 10 minutes more. (For a gas grill, preheat grill. Reduce heat to medium. Adjust for indirect cooking. Place foil pan on grill rack over burner that is off. Grill as above.) Cool on wire rack for 30 minutes. Serve warm. Makes 6 servings.