Preheat the oven to 225C/440F/Gas 8.
Place a heavy baking tray into the oven to preheat.
Mix the flour, salt and icing sugar in a large bowl. Make a well in the middle of the dry ingredients and pour the egg into it. Scoop a liberal amount of flour over to cover the egg.
Place the water, butter and lard into a saucepan over a low heat and bring slowly to the boil.
Gradually pour the boiling liquid into the flour mixture, stirring with a knife constantly to combine, then knead on a clean, floured surface until the egg is completely combined and the pastry is smooth. (NB: use the pastry immediately to make your pie because when the pastry cools it will harden and become unmanageable.)
Cut off one third of the pastry and set this aside for the lid. Roll out the remaining pastry into a flat round shape large enough to line the base and sides of a 25cm/10in loose-bottomed cake tin, allowing an overhang of pastry of about 2cm/1in.
Roll out the pastry set aside for the lid to fit the top of the pie and set aside.
For the filling, heat a frying pan until hot, then add the butter, leeks and thyme and gently fry for 5-8 minutes, or until the leeks are tender. Set aside and allow to cool slightly.
Place the lamb into a food processor along with the parsley and mint leaves and pulse to chop finely. Season well with salt and freshly ground black pepper.
Spread the lamb mixture into the pastry case in a thick layer and then spread the leeks over the top.
Brush the edges of the pastry with a little beaten egg. Place the pastry lid on top of the filling and pinch and crimp the edges of the case and lid together to seal.
Trim away any excess pastry from the pie with a sharp knife and use the pastry trimmings to make decorative leaves for the top of the pie.
Brush the top of the pie with beaten egg and make a hole in the centre to allow the steam to escape. Arrange the pastry leaves on top and brush these with the beaten egg.
Place in the oven to cook for 15 minutes, then reduce the oven temperature to 180C/355F/Gas 4 and continue to bake for one hour. Remove from the oven and allow to cool for five minutes before serving.
To serve, cut out a wedge of pie and place onto a plate accompanied by buttered new potatoes and chantenay carrots.