In a small saucepan, combine equal parts sugar and water, along with the fresh lemon juice. Heat over medium-high heat, stirring until the sugar completely dissolves. Allow the mixture to simmer for about 5 minutes until slightly thickened. Remove from heat and let it cool.

In a medium saucepan, whisk together fine semolina, whole milk, and sugar over medium heat. Continuously stir for about 8-10 minutes until the mixture thickens. Remove from heat and whisk in the egg yolks, vanilla extract, and melted butter until smooth.

Preheat your oven to 350°F (175°C). Unroll the phyllo dough and cover it with a damp towel. Layer the phyllo in a greased baking tray, brushing each sheet with melted butter. Use about 8-10 sheets for the base.

Pour the creamy custard over the layered phyllo base, cover with additional phyllo layers while brushing with butter, ensuring there are at least 6 layers on top. Tuck the edges in gently.

Place the assembled Galaktoboureko in the preheated oven and bake for approximately 45-50 minutes or until the top is golden brown. Remove from the oven and let cool slightly.

Immediately pour the cooled syrup evenly over the hot pastry. Allow to rest for at least one hour before cutting into squares or diamonds.