For the tzatziki sauce, add all ingredients to a medium bowl. Stir to combine. Taste and adjust the seasonings if necessary. Set aside while you make the gyros. The sauce can be made the day before and is best if it sits for a few hours, though it can be eaten immediately.
For the gyros: Pull out two skillets, one large for the lamb and one medium to warm the pitas. Add the lamb to the large skillet and saute the lamb over medium heat until warmed through, 5 minutes.
While the lamb is warming, heat the medium skillet over medium heat. Add a little olive oil to the skillet (enough to coat the bottom). Add the pita to the skillet and warm it for 30 seconds, then turn it over and warm it for another 30 seconds. Repeat for the other three pitas, adding more olive oil as needed.
Set out the tzatziki sauce, onion, lettuce, tomato, lamb, warmed pitas, and any optional additional toppings so everyone can assemble their own gryo.