To make the syrup: In a medium saucepan, whisk together the honey, water, sugar, and cinnamon stick. Use a vegetable peeler to remove the zest of the lemons in large pieces and add to the syrup mixture. Squeeze the lemons, discard the seeds, and add the juice to the syrup.

Bring to a boil, lower the heat, and simmer until slightly thickened, about 35 minutes. Remove from the heat and set aside to cool slightly. Remove and discard the cinnamon and lemon zest.

To make the filling: In a food processor, combine the nuts, cinnamon, allspice, and salt; pulse until finely chopped (don't over chop!). Transfer the nut mixture to a bowl and set aside. In a medium saucepan, completely melt the butter over medium heat. Set aside for 5 minutes, then skim the white foam from the surface of the butter and discard. Pour the clear butter into a small bowl, stopping before the watery liquid on the bottom pours in. Discard the watery butter in the bottom of the pan. Stir 1/2 cup of the syrup into the nut mixture. Set the remaining syrup aside.

To assemble the baklava: Preheat the oven to 350 degrees F.

Place a piece of parchment paper in a 10 by 14-inch baking dish. (The edges of the parchment should come half way up the sides of the dish.)

Unroll the phyllo onto the work surface, and place the stack off to 1 side. Lift 1 sheet and lay it on the workspace, lengthwise, and parallel to the edge of the counter. Brush the sheet with some of the butter. Lay another sheet on top, and brush with butter; repeat with 1 more sheet. Mound 1/6 of the nut mixture, lengthwise, about 1-inch from the bottom edge and ends. Roll the bottom edge of phyllo over the nut mixture, fold in the sides to seal the log, and continue rolling until completely closed. Place the phyllo roll seam side-down in the baking dish. Repeat with the remaining ingredients to make 6 rolls in all, arranging them in snug rows.

Brush the top of the rolls lightly with water. Using a paring knife, lightly score the rolls, crosswise, at 3-inch intervals. Bake until golden brown, about 40 minutes.

Rewarm the syrup over medium heat. Cut through the scored lines of the pastry and pour the syrup over the warm pastry. Set aside to cool for 1 hour.