Preheat the oven to 400°F (200°C) and line two baking sheets with parchment paper.
In a bowl, beat the cream cheese, granulated sugar, egg, vanilla extract, and lemon juice until smooth and creamy.
Unfold the puff pastry and cut each sheet into 4 squares to make 8 pieces total. Place the squares on the prepared baking sheets.
Spoon a portion of the cream cheese filling into the center of each square, then fold or shape the pastry as desired, leaving the filling exposed if preferred.
Brush the pastry edges with egg wash and sprinkle with coarse sugar if using.
Bake for 16 to 18 minutes, or until the pastry is puffed and golden brown and the filling is set.
If desired, whisk the powdered sugar with enough milk to make a glaze and drizzle over the cooled danishes before serving.