Combine sugar and water in a saucepan over medium high heat. Bring to a boil, then reduce heat to medium and simmer for 7-10 minutes until it has started to thicken. Turn the heat off, stir in the lemon juice and set aside to cool completely.
Mix the finely chopped walnuts with cinnamon and set aside.
Preheat oven to 350°F (175°C). Brush a 9x13-inch baking pan with some of the melted butter.
Place one sheet of phyllo on a clean surface. Keep the remaining sheets covered with a towel. Brush the sheet generously with melted butter.
Sprinkle 2 to 3 tablespoons of the walnut mixture evenly over the surface, leaving a small border at the edges.
Place the dowel at the bottom edge and roll the phyllo tightly around it. Gently push both ends inward toward the center to scrunch the roll. Slide the dowel out and place the roll in the prepared pan.
Repeat with the remaining phyllo sheets and filling.
Cut each roll into half. Brush the tops generously with more melted butter.
Bake for 40-45 minutes until deeply golden.
Immediately pour the cold syrup evenly over the hot baklava. Let sit for 2 hours until fully absorbed before serving.