First, make the tzatziki. Combine all ingredients in a small mixing bowl and stir until well-incorporated. If you have time, cover and chill the mixture for at least 30 minutes, or up to overnight.
To make the eggplant, heat the olive oil in a medium saute pan over medium-high heat. Add eggplant and garlic and stir to combine. Cook until eggplant is tender, adding more olive oil as needed, then season with salt, pepper and lemon juice. Remove from pan and set aside.
To make the lamb, heat another 2 tablespoons of olive oil over medium-high heat (using the same saute pan.) Add the lamb, garlic and fresh oregano and cook until lamb is browned. Season with salt, pepper and lemon juice. Turn off heat and set aside.
Preheat the oven to 350 degrees Fahrenheit. Spread the pita chips evenly over the bottom of a medium cast iron skillet. Sprinkle the eggplant, lamb, garbanzo beans, cheese, cherry tomatoes and red onion evenly over the top. Place in the oven for approximately 12 minutes, and then turn the broiler on high for an additional 3-5 minutes, or until the cheese on top is starting to brown.
Remove the cast iron skillet from the oven, being careful to use potholders, and drizzle on tzatziki (you don’t have to use it all, just use however much you want.) Sprinkle with more fresh oregano before serving straight out of the pan!