Stir 1 1/4 cups granulated sugar, the lemon juice and peaches in a large pot; let sit 15 minutes. Bring to a simmer over medium-high heat, then reduce the heat to low and cook until the peaches are tender, about 15 minutes. Remove 3/4 cup peaches with a slotted spoon and refrigerate for topping. Puree the remaining peaches and cooking liquid in a blender; transfer to a bowl and freeze until very thick, about 1 hour.
Meanwhile, preheat the oven to 350 degrees F and line a baking sheet with foil. Coarsely crush the graham crackers and toss with the remaining 1/4 cup granulated sugar, the pecans and butter on the prepared baking sheet; spread into a thin layer. Bake 7 minutes, then stir and continue baking until golden brown, 6 to 10 more minutes. Let cool and harden, then crumble and set aside.
Assemble the cake: Let 2 pints ice cream soften at room temperature until spreadable, about 10 minutes. Coat a 9-inch springform pan with cooking spray and line the bottom and sides with plastic wrap, leaving a 2-inch overhang. Spread the softened ice cream in the prepared pan, then top evenly with the peach puree. Freeze until the puree is firm, about 45 minutes.
Let the remaining 2 pints ice cream soften, 10 minutes, then spread over the peach puree. Sprinkle with 1 cup of the pecan mixture and press it into the ice cream. Cut the pound cakes lengthwise into 1 1/2-inch-thick slices; arrange the slices in a single layer on top of the ice cream, trimming as needed. Cover with plastic wrap and freeze until firm, at least 6 hours or overnight.
Beat the heavy cream, confectioners' sugar and vanilla in a bowl with a mixer on medium speed until soft peaks form. Uncover the cake, then invert onto a plate; remove the springform ring and the remaining plastic wrap. Cover the top and sides with the whipped cream. Top with the reserved peaches and remaining pecan mixture. Freeze until firm, about 1 hour.