Combine the sugar and water in a saucepan over medium-high heat.
Bring to a boil, then reduce the heat and simmer for 25 minutes.
Stir in the lemon juice.
Cool the syrup, then refrigerate it until cold.
Heat the oven to 350 degrees F.
Brush a 9-by-13-inch baking dish with clarified butter.
Trim the phyllo sheets to fit the dish.
Keep the stack covered with a damp kitchen towel while you work so the sheets dont dry out.
Place one sheet of phyllo in the dish and brush it lightly with clarified butter.
Repeat until you have a stack of 10 buttered sheets.
Sprinkle half of the 3 cups of chopped pistachios evenly over the phyllo.
Add another stack of 10 phyllo sheets, brushing each sheet with clarified butter as you layer it.
Bake for 60 minutes, or until the top is golden brown.
After 40 minutes, loosely cover the dish with foil to keep the top from browning too quickly.
Remove the baklava from the oven and immediately pour the cold syrup evenly over the hot pastry.
Sprinkle the remaining chopped pistachios over the top.
Let the baklava cool completely before serving.