Preheat the oven to 325°F Prep a spring form pan as follows: Place a sheet of parchment paper over the inside bottom of the springform pan, fit the rim and lock in place. Trim excess paper from the underside of the pan. Place two large sheets of heavy duty aluminum foil on counter. Place the locked pan in center and raise up the foil to top rim. Crinkle around the outer top of rim.
CRUST: Combine graham cracker crumbs, sugar, and butter in a small bowl, mix well. Butter the bottom and inside edges of a spring form pan and coat the bottom about 1/4 inch thick and the sides about 1/8 inch thick with the crust mixture. Refrigerate while making the cake batter.
CAKE: In a bowl, beat cream cheese, sugar, and sour cream until soft and smooth. Add the eggs and beat until combined. Then add the vanilla and lemon juice and mix thoroughly.
Pour the batter into the prepared pan and place the cake pan inside a water bath (which is a large roasting pan and pour in very hot tap water until it reaches halfway up the sides of the cake pan.). Bake for 1.5 hours, or until the center reaches 145°F with an instant read digital thermometer.
TOPPING: Increase oven temperature to 400°F Combine the sour cream, sugar and vanilla and pour over the top of the cheese cake and bake for 15 minutes more.
Remove the cake pan from the larger pan and set aside to cool on a rack. Then refrigerate for at least 4 hours.
CARAMEL TOPPING: In double broiler melt caramel candies.
In a small bowl combine powdered sugar and milk, adding more sugar if needed so mixture is thick enough to coat a spoon. Add peaches to caramel, then add milk and sugar mixture until you reach thickness that you desire. (Do not overcook.).
Cool topping to room temperature, then top the cheese cake and refrigerate at least 4 more hours. Do not release spring. Refrigerate a minimum of 4 hours.
SERVE: Run a knife between the cake and the rim of the pan. Release the spring, and carefully lift off the rim.