Prepare a large baking sheet by lining it with parchment paper.
In a stand mixer, beat the cream cheese until creamy and smooth. Mix in the sugar, vanilla, lemon juice, and graham cracker crumbs. Combine this well.
Scoop out 1 Tablespoon of the mixture at a time and scrape into a mound. (They don't have to be perfectly round.) Place each ball onto the parchment paper lined baking sheet. Place the sheet of cheesecake balls into the freezer for at least 30 minutes.
Place the 4 cups of oil into a heavy bottom pot (it should be at least 2 inches deep). Turn this on to medium heat. As this is heating, prepare the batter.
Whisk the flour, sugar, and baking powder together in a medium bowl. Then whisk in the milk until smooth.
When the oil is heated to 365 °F (185 °C), place a baking sheet lined with paper towels next to the pot of oil.
Remove the frozen cheesecake balls from the freezer. If you want to round them out more, this is the time to do it, but handle them as little as possible so they stay firm. Use a slotted spoon to dip them a few at a time into the batter, turning to coat.
Then place the coated balls into the hot oil, no more than 3 at a time. (Don't do too many at a time as it will bring down the heat of the oil too much.) Turn them to brown evenly. This will take about 2-3 minutes per side. Remove them from the oil with tongs and place them on the paper towel lined baking sheet.
Serve them plain or with jam or chocolate sauce. They are also delicious with powdered sugar sprinkled on top.