Crumble the yeast and add the sugar and about 3 1/3 tbsp (50 ml) warm water to it. Stir well and add 2 tbsp flour, stir again and wait for the yeast to bubble.
In the meantime, beat the yoghurt with 2 whole eggs + the whites of the other 2 eggs. Set aside the remaining yolks for smearing the pita before baking.
Cut half the butter into cubes and melt it with the lard. In a bowl, mix the yoghurt mixture, bubbled yeast and lard with the salt well. Gradually add the flour and knead until you get a soft dough that doesn't stick to your hands.
Divide it into 3 equal-sized parts and leave them to rise. Remove the pits from the olives and cut them finely.
Take a 16″ (40 cm) diameter cake form and lay it out with baking paper. Smear your work surface with butter and roll out each of the dough parts thinly, smear with butter, sprinkle with olives, feta cheese and grated cheese.
Roll up into a roll and put it in the cake form, starting from the middle. Do this for all of the dough parts. Leave the pita to rise once again and then smear with the set aside egg yolks.
Bake in a preheated 320°F (160 °C) oven about 20 min., then turn up the oven to 374°F (190 °C) and bake until it gets a nice, golden color. Once you take the pita out of the oven, smear it with butter and wrap with a towel.