Make the pita bread. Combine yeast, sugar and warm water in the base of a large bowl. Mix together and let rest for about 5 minutes covered with a damp tea towel until frothy. Add flour, oil and salt and mix either by hand with a wooden spoon, or using a dough hook attachment on your stand mixer, until the dough comes together. Turn the mixture out onto a lightly floured surface and knead for a few minutes, adding more flour if the mixture is too sticky, until you get a smooth dough. Place the dough back in the mixing bowl that has been lightly oiled and turn the dough until it is coated in the oil. Cover with a damp tea towel and leave in a warm spot for 45-60 mins until the dough has doubled in size.
Marinate the lamb. While the dough is rising, cut up the lamb into strips and and place into a bowl. Finley chop the garlic and add to the bowl along with the olive oil, herbs, salt and lemon zest. Mix everything together, cover with plastic wrap and place in the fridge while you finish the bread.
Once the pita bread dough has risen, punch it down and turn out onto a floured surface. Knead again until the dough is smooth. Shape into a ball and cut evenly into 8 pieces. Roll each piece into a ball and using a rolling pin roll out the dough into circles about 15 cm in diameter one at a time. Make sure to keep any dough that you are not working with covered with the damp tea towel so it doesn’t dry out.
Heat your skillet on the stove with a tablespoon of olive oil. Once hot, add the dough one at a time, cooking for about 2 minutes until the bread is puffing and bubbling and the bottom is golden. Turn and cook for another minute. Repeat until all bread is cooked and set aside.
Wipe out the skillet with a paper towel and add the lamb strips, cooking for a couple of minutes until brown and just cooked through.
Assemble. Spread a spoonful of the baba ganoush dip on the middle of a pita. Top with a few lettuce leaves and the lamb. Drizzle with the lemon mayo and some chopped parsley.