Make the syrup first: Combine granulated sugar, water, and lemon juice in a small saucepan. Bring to a boil over medium heat, then reduce to a lively simmer and cook 10–12 minutes until slightly thickened and it lightly coats the back of a spoon. Cool completely to room temperature.
Melt unsalted butter in a small saucepan over low heat until separated; skim off foam and pour the clear fat into a bowl, leaving the milk solids behind. Keep the fat warm.
Prepare the nut mixture: Pulse walnuts in a food processor to a fine, pebbly chop (do not puree). Set aside.
Prepare the pan and dough: Heat oven to 325°F. Brush a 9×13-inch baking pan with a little of the warm fat. Unwrap phyllo dough, trim to fit the pan if needed, and keep covered with a barely damp towel to prevent drying.
Assemble the layers: Lay one sheet in the pan and brush lightly with fat; repeat to build 10 sheets. Evenly sprinkle one-third of the nut mixture over the surface. Add another 10 sheets, brushing each with fat; sprinkle half of the remaining nut mixture. Add a third set of 10 sheets, brushing each; top with the last of the nut mixture. Finish with a final 10 sheets, brushing each and the top surface.
Cut before baking: With a very sharp knife, cut the pastry into 4–5 long strips, then cut on the diagonal to form diamonds, making sure to cut all the way to the bottom.
Bake until deep golden and crisp, 60–75 minutes, rotating the pan once; edges will be well browned and the top will sound crisp when tapped.
Syrup the pastry hot: Immediately after removing from the oven, slowly pour the cooled syrup evenly over the hot pastry, focusing on the cut lines; it should sizzle slightly. Let stand uncovered at room temperature until the syrup is absorbed and the pastry is set, 4–6 hours or overnight.
Finish and serve: Sprinkle pistachios over the top (for serving), then lift pieces out along the cut lines. Store covered at room temperature for up to 3 days.