Mix the zaatar and olive oil in a bowl and set aside.
Preheat the oven to 500 degrees F and lay a baking tray in the oven to heat.
Cut the Lebanese Pita Dough into 12 pieces. Roll out the dough to 1/4- inch thick. Pinch the edges around the dough to form higher edges. Take a fork and pierce the dough all over, releasing any air pockets. Spread 1 to 2 tablespoons za'atar (make sure you mix before using) over each pita dough. Place 3 to 4 pitas on the hot baking tray in the oven and close the door immediately, making sure to not overcrowd the baking tray or oven. Bake until golden on the bottom and a little golden on the top, about 5 minutes. Serve with labneh, tomatoes and black olives rolled inside. The perfect Lebanese breakfast!
Sift the flour, yeast, salt, and sugar together. Make a well in the middle of the dry mixture. Pour in the lukewarm water. Mix by hand on a floured work surface until the dough comes together. Then knead the dough for 10 to 15 minutes until smooth and the dough bounces back when you push into it. Drizzle the dough with olive oil and place in a warm spot covered with a damp towel. Let rise until the dough doubles in size, depending on the temperature, it could take 30 minutes to 1 1/2 hours.