COOK IT.
For the black raspberry sauce, combine raspberries, sugar and lemon juice in a medium saucepan, simmer over medium heat for 10-15 minutes, stir constantly. Strain and crush the fruit to release as much juice as possible. Discard pulp and seeds.
Immerse peaches in a large pot of boiling water for 1 minute to loosen skins. Remove from water and peel. Cut in half and remove the pits. In a small glass bowl, whisk together the juice of 2 limes and honey. Pour over peaches and allow them to marinate for a 1/2 hour. Meanwhile, preheat barbecue on HIGH for 5 minutes and brush grids generously with vegetable oil. Reduce heat to MEDIUM. Grill peaches for 3 minutes, baste with remaining lime and honey mixture, turn and grill another 3 minutes.
Remove from heat, let cool slightly and serve with a scoop of vanilla ice cream, topped with 2 Tbsp. of raspberry sauce and 1 tsp. toasted almond slivers.