Allow the puff pastry dough to defrost according to the package directions.
Preheat the oven to 350°F and line 2 baking sheets with parchment paper.
Place the sugar and cinnamon in a small bowl and stir to combine.
Unfold one sheet of puff pastry dough onto a clean counter with the long side facing you.
Spray the dough with nonstick spray and sprinkle 2 tablespoons of cinnamon sugar onto the dough.
Using a pizza cutter, cut the dough in half horizontally. Then cut the dough vertically into 10 pieces.
Twist each piece of dough 2 to 3 times and place them onto the parchment-covered cookie sheet. Sprinkle with an additional 1 tablespoon of cinnamon sugar.
Repeat the process with the second sheet of pastry dough.
Bake for approximately 15 minutes or until the dough appears toasted.
To prepare the icing, use an electric mixer to beat the softened cream cheese and margarine together. Slowly add the powdered sugar, lemon juice, and vanilla extract and beat until smooth.
Serve the Cinnabon Stix with a small bowl of icing on the side.