To make the syrup, add the sugar, water and lemon juice to a pan set over a low to medium heat.
Bring it to a boil, and leave to simmer for 15 minutes until slightly thickened.
Leave to cool completely.
Melt the butter over a low to medium heat. If you want to get clarified butter, use a spoon to remove the white foam that forms over the butter when it melts - or you can just leave it, it's entirely optional.
Shell the pistachios, then either chop them finely, or blitz them in a food processor.
Brush butter over the bottom of a large rectangle baking tray - mine is 40x27cm, or 15x10 inches.
Arrange a sheet of phyllo pastry over the buttered tray, and brush it with more melted butter.
Repeat with 7-8 more sheets of pastry.
Sprinkle a third of the pistachios over the 8th sheet of phyllo, then repeat the process with other 7-8 sheets of buttery phyllo.
Sprinkle another third of pistachios, then again repeat with 7-8 more sheets of pastry.
Preheat the oven to 180 degrees Celsius (350 Fahrenheit).
Slice the baklava into squares - I got 7x5 squares, so 35 in total.
Bake for 20 minutes on the middle rack of the oven, then lower the temperature to 150 degrees Celsius (300 Fahrenheit).
If the baklava browns too quickly, cover it well with kitchen foil.
Bake for a further 25-30 minutes until the top with crispy and golden brown, and all the layers are baked through.
Pour over the cooled syrup, and sprinkle the remaining pistachios all all over the top.
Leave to cool overnight.