In a large bowl, use an electric mixer to combine the cream cheese, lemon juice, and vanilla extract.
Once smooth, use a spatula to scrape down the sides of the bowl, then add the sugar and heavy cream. Mix on high speed for about 2 minutes, or until the batter is thick and smooth.
Pour batter into a 13x9-inch (33x23-cm) baking dish lined with parchment paper. Use a spatula to spread the batter evenly and make the top as level as possible.
Freeze for four hours.
Fill a gallon-size plastic bag with the graham crackers. Use a rolling pin or meat mallet to crush the graham crackers until they are super-fine crumbs.
Pour the flour, eggs, and graham cracker crumbs into 3 separate medium bowls.
Heat the oil in a large pot until it reaches 350°F (180°C).
Remove the cheesecake batter from the freezer and use the parchment paper to lift it out of the pan. Cut the cheesecake into 12 4x3-inch (10x7-cm) bars.
Take a piece of cheesecake and toss it in the flour. Tap off any excess flour, dip the piece in the egg, and then toss it in the graham cracker crumbs. Dip it back in the egg again, then toss in the graham cracker crumbs once more. Repeat with the remaining cheesecake pieces.
Fry the breaded cheesecake, 2 or 3 bars at a time, until golden brown, 30–60 seconds.
Drain the cheesecake bars on a wire rack or paper towels.
Serve with strawberry sauce, whipped cream, and powdered sugar.