Finely chop up 1/2 of the garlic on a cutting board and sprinkle with a generous pinch of salt. Mash the garlic and salt together with the flat-side of a knife into a paste. Add the oregano and continue to mash until incorporated. Put the garlic-oregano paste in a small bowl, add the lemon juice and 1 cup of olive oil; season with salt and pepper. Slice the remaining garlic into thin slivers.
Put the lamb on a large platter, and trim any excess fat. Cut the lamb in 1/2 lengthwise so you have 2 large pieces. Make slits all over the meat with a sharp knife, and push the garlic slivers inside. Rub 1/2 of the garlic-oregano paste all over the lamb and season the meat with salt and pepper. Roll up each piece of lamb lengthwise and tie with butcher's twine to hold the roasts together. Put the lamb on a large platter and slather with the remaining garlic-oregano paste. Marinate, covered, in the refrigerator for at least 1 hour or up to overnight.
Preheat the oven to 375 degrees F.
Wipe off the excess paste from the lamb so it won't burn in the oven. Place a large roasting pan over 2 burners on medium-high flame and coat with a fair amount of olive oil. Put the lamb roasts in the roasting pan and sear to form a nice brown crust on all sides. Transfer the pan (and lamb) to the oven and roast for 1 to 1 1/2 hours; it should be pink in the center and the internal temperature reads 130 degrees F. Allow the lamb to stand 10 minutes to let the juices settle before and slicing.
Cut off the butcher's twine and thinly slice the lamb. Place the meat in the center of the pita breads. Top with lettuce, chopped tomatoes, and tzatziki.
Put all the ingredients in a mixing bowl and combine with a fork. Refrigerate for at least 1 hour to allow the flavors to marry.