Prepare the cake mix according to the package directions and bake it in a 9x13-inch baking pan for the recommended time. Test the center with a toothpick; it should come out dry and clean.
Remove the cake from the oven and use the handle end of a wooden spoon to poke large holes all over the cake. Let the cake cool while preparing the peach filling.
Place the peeled peach chunks into a food processor or blender and pulse until partly pureed, leaving some larger pieces if desired.
Add the peach puree, granulated sugar, and lemon juice to a saucepan over medium-high heat. Stir and bring to a low boil for 3 to 4 minutes, until the sugar dissolves and the mixture thickens slightly.
Remove the peach filling from the heat and pour it evenly over the cake, guiding the mixture into the holes.
Cover the cake and refrigerate for 2 hours.
Beat the softened cream cheese and granulated sugar together in a large mixing bowl until smooth.
In a separate bowl, beat the heavy whipping cream and powdered sugar until stiff peaks form, about 5 minutes.
Fold the whipped cream into the cream cheese mixture until combined.
Spread the cream topping evenly over the chilled cake. Cover and refrigerate for at least 4 hours before serving.
Top the cake or individual slices with fresh peach chunks right before serving.
