Make the syrup first so it cools: combine sugar and water in a pan. Bring to a boil, stirring to dissolve the sugar. Simmer for 10 minutes. Add the rose water and lemon juice. Cool completely.
Preheat oven to 180°C (350°F). Brush a 33 x 23 cm baking tin with butter.
Mix the chopped nuts with cinnamon and cardamom.
Layer half the filo sheets in the tin, brushing each sheet generously with melted butter.
Spread the nut mixture evenly over the filo. Layer the remaining filo sheets on top, brushing each with butter.
Using a sharp knife, cut the baklava into diamond or square shapes, cutting all the way through to the base.
Bake for 35–40 minutes until deeply golden.
Immediately pour the cold syrup over the hot baklava. Allow to absorb for at least 1 hour before serving.