Mix butter and lard in a bowl, then rub a quarter of the mixture into the flour and salt.
Add 50ml cold water and lemon juice to form a dough and shape into a rectangle.
Roll dough to a rectangle, dot with remaining fats, and perform a series of folds and rotations.
Chill the dough in cling film for 20 minutes.
Prepare mint sauce by chopping mint with salt, adding 100ml boiling water and sugar, then cooling with vinegar.
Roll and fold the chilled pastry once more and refrigerate for another 20 minutes.
Mix lamb with garlic, rosemary, and half the mint sauce; season and set aside.
Combine vegetables and herbs with the remaining mint sauce and peas.
Preheat oven to 180°C and line two trays with parchment.
Roll pastry to 3mm thickness and cut into 6 circles of 13cm diameter.
Fill circles with vegetables and lamb, moisten edges, fold over, and crimp to seal.
Brush pasties with egg and bake for 40 minutes until golden.
Cool pasties on a wire rack before serving.