In a medium pot, combine sugar, lemon juice, and water. Simmer over medium heat until the sugar dissolves, then set aside to cool completely.

In a saucepan, whisk together milk and semolina over low heat, stirring continuously until thickened (about 10-15 minutes).

Add sugar, eggs, melted butter, and vanilla extract, mixing until smooth. Allow it to cool slightly.

Layer several sheets of phyllo dough in a well-greased baking dish, brushing each sheet with melted butter.

Pour the custard mixture over the phyllo layers, then cover with additional phyllo sheets, brushing with butter.

Bake in a preheated oven at 350°F (175°C) for about 40-45 minutes, or until the top is golden brown.

Immediately after baking, pour the cooled syrup over the hot Galaktoboureko.

Allow to cool completely at room temperature before slicing it into squares.