Heat the oil in a 12-inch skillet over medium heat.
Mince garlic and chop onion; add to skillet and cook until tender, stirring occasionally.
Add the spinach and cook for 5 minutes or until wilted. Remove the spinach mixture from the heat and let cool to room temperature, then drain well in a colander, pressing to squeeze out any excess liquid. Return the spinach mixture to the skillet. Grate the cheese and add to the skillet along with the lemon juice.
Preheat the oven to 400°F.
Beat the egg and water in a small bowl with a fork.
Sprinkle your work surface with the flour. Unfold 1 pastry sheet on the work surface; roll into a 12-inch square, then cut into 8 (3-inch) squares. Repeat with the remaining pastry sheets.
Brush edges of the squares with the egg mixture, then place about 2 teaspoons spinach mixture in the center of each. Fold the pastry over the filling to form triangles. Press the edges to seal, then crimp the edges with a fork.
Place the filled pastries onto 2 baking sheets; brushing more of the egg mixture over top.
Bake for 20 minutes or until the pastries are golden brown. Transfer to a cooling rack and let cool before serving.
Serve with orange wedges on the side.