Heat a grill to medium-high heat.
Place 3/4 cup sugar, the water, 1 tablespoon of the lemon juice, and the seeds from the vanilla bean into a small saucepan and set over high heat. Bring the mixture to a boil and boil for 1 to 2 minutes. Remove from the heat. Add the peaches, spooning the sauce over them. Set aside.
Place the raspberries, the remaining 1 tablespoon of lemon juice, and 1 tablespoon sugar into the bowl of a food processor and puree. Pass the mixture through a fine-mesh sieve into a small bowl. Cover and set in the refrigerator.
Once the grill is hot, place the peaches over direct heat and grill until they are tender, 3 to 4 minutes per side. Remove from the heat to a container with the syrup and cover with aluminum foil for 5 minutes.
To serve, place the ice cream into 4 bowls and top each bowl with 2 peach halves. Drizzle each bowl with the raspberry sauce and serve immediately.