In a mixing bowl, combine the softened cream cheese, powdered sugar, and vanilla extract. Beat with a hand mixer or stand mixer until smooth and creamy.
Add the diced strawberries and lemon juice to the cream cheese mixture. Gently fold in the strawberries until evenly distributed.
Lay out one flour tortilla on a clean surface. Place about 1/4 cup of the strawberry cheesecake filling in the center of the tortilla.
Fold the sides of the tortilla over the filling and roll it up tightly, similar to a burrito. Repeat with the remaining tortillas and filling.
Heat about 1 inch of vegetable oil in a frying pan over medium heat. Once hot, carefully add the chimichangas, a few at a time. Fry until golden brown on all sides, about 3-4 minutes.
Remove the chimichangas from the oil using tongs and place them on a paper towel-lined baking sheet to drain excess oil.
In a small bowl, mix the granulated sugar and ground cinnamon together. While the chimichangas are still warm, sprinkle the cinnamon sugar mixture over them.
Serve warm with whipped cream or additional strawberries, if desired.