In the jar of a high-powered blender, purée 5 cups peaches, sugar, and lemon juice. Pour into an ice cream machine and follow manufacturer’s directions. Freeze mixture for a few hours, until sorbet firms up.

Line a 9- by 5- by 3-inch loaf pan with plastic wrap. Spread a ¼-inch-thick layer of sorbet on the bottom and 4 sides of pan to the edges; return to freezer.

In a skillet, heat 2 cups peaches, sugar, and lemon for 1–2 minutes, until peaches are warmed through. Drain and set aside to cool.

Remove pan from freezer and spread 1 pint of vanilla ice cream in an even layer. Return to freezer for at least 1 hour. Next, add the peach filling layer and return to freezer for another hour. Follow with another layer of vanilla ice cream and freeze again for an hour.

Complete with a final ¼-inch-thick layer of peach sorbet, fully to edges, and freeze for an additional hour, or until ready to serve.