1. Prepare the syrup. In a saucepan, put 1 2/3 cups of water and the sugar (1 cup) then bring to a boil, stirring regularly with a wooden spoon, until the sugar is completely dissolved. Let the syrup thicken and reduce by a quarter in volume (about 10 to 20 minutes).
Add the lemon juice. Let it cool.
2. Prepare the walnuts. Crush the walnut kernels with a pestle or in a food processor without reducing them to powder. Mix them with the sugar in a bowl.
3. Proceed with the assembly. Melt the butter in a saucepan over very low heat. Let it warm up. Take half of the phyllo pastry sheets and keep the others under a slightly damp cloth to prevent them from drying out. Butter a high-sided baking dish. Spread a first sheet of phyllo pastry at the bottom of the dish, then brush it with melted butter using a brush.
Proceed in the same way for the rest of the sheets taken (reheat the butter if necessary; it should always be warm to make it easier to spread). Spread the walnut filling evenly. Layer the remaining sheets in the same way, buttering them between each layer.
4. Make the cuts. Preheat the oven to 180°C (350°F). Cut into diamond shapes using a sharp knife: cut the pastry into strips about 5 cm wide and then diagonally. Brush with melted butter again. Bake for about 25 minutes (the top should be golden brown). Let it cool slightly.
5. Finish. Pour the cooled syrup over the baklava, adjusting the amount according to your preferences (be careful not to soak it too much; remove any excess if necessary). Serve the dessert without delay or enjoy it the next day (it's even better).