Place the warm water, yeast, sugar, and ½ cup flour in a large bowl and mix to combine. Let it stand for about 15 minutes to get foamy.
Add the salt oil and remaining 2 cups of flour and mix with a spoon until it starts coming together. It will be a bit shaggy. Tip this out onto a floured surface and knead for around 8 minutes until you have a smooth dough. Add a little extra flour if necessary and to prevent sticking.
Put the dough ball into a clean bowl, cover with cling wrap, and place in a warm spot to rise for about an hour. It should double in size.
Tip the proved dough back onto a surface and divide it into 8 even-sized pieces. Roll these into balls and place them on a tray and cover them with a tea towel and allow to rest for 15 minutes.
Preheat the oven to the highest it can go – 250C / 500F and place a pizza stone in the middle. If you don’t have a pizza stone, you could preheat a very thick oven stray or cast-iron skillet.
When the oven and stone are preheated, roll each piece of dough into thin rounds about 20cm (8 inches) in diameter. Place as many as you can on the stone and bake for around 4-5 minutes. They should start puffing up almost immediately. Once puffed up quickly remove and bake the others. Wrap them in a clean tea towel as they come out of the oven.
Serve the pita bread with the grilled lamb souvlaki, tzatziki, lemon wedges, mint, tomato, and cucumber salad (or any other salad of your choice).