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Make the Syrup
Stir the sugar and water in a pot until the sugar dissolves, then bring to a boil. Add the lemon juice, stir once and take the pot off the heat. Let it cool completely. The syrup must be cold when it meets the hot baklava.
Make the Dough
Whisk the flour, egg, oil, milk and salt in a bowl with a fork, then knead by hand until soft. If it sticks to your hands, add 1 tablespoon of flour. Cover with a clean cloth and rest 10–15 minutes.
Divide the Dough
Cut the rested dough into 20 equal pieces and roll each into a ball. Keep them covered.
Roll the First Stack
Dust your counter generously with cornstarch. Roll 10 pieces, one at a time, to about the size of a small plate, dusting with cornstarch each time. Stack the 10 sheets with cornstarch between them.
Roll to Fit the Dish
Roll the whole stack together, turning it, until it is as wide as your 12.5-inch round glass baking dish. Use the dish as a guide and trim the extra edge with a knife. Lift the 10 sheets into the dish one by one.
Add the Walnuts
Spread the chopped walnuts evenly over the sheets.
Add the Top Layers
Roll the remaining 10 pieces the same way and layer them over the walnuts.
Cut
Preheat the oven to 340°F (170°C). Cut the baklava into 12 triangle slices before baking, cutting all the way through.
Add the Butter
Pour the melted butter evenly over the cut baklava.
Bake
Bake for about 50–60 minutes, until golden.
Add the Syrup
Pour the cold syrup slowly over the hot baklava right out of the oven. Let it cool and soak for several hours before serving.