Preheat the oven to 325 degrees F. Lightly grease a 7 ½ x 11 baking pan with olive oil.
In a food processor, add the ingredients for the lamb and process until everything is well mixed and the same consistency.
Spread the meat onto the baking pan and pat into an even layer reaching all the sides.
Place the baking pan on a baking sheet and place on the middle rack of the oven. Add some boiling water to the baking sheet to create a shallow water bath for the baking pan.
Bake for about 60 minutes. Allow to cool to room temperature, then drain the liquid. Wrap tightly, and refrigerate for a few hours to help the flavors develop.
As the eat is cooling, make the tatziki.
Take the meat from the refrigerator and cut into thin slices.
Heat a skillet with a small amount of olive oil and add in the meat in batches, cooking for about a minute on each side.
Spread tatziki on the pita, and layer meat, and the other assembly items. Wrap the pita tightly. Use parchment paper to tightly wrap around the pita to secure it.