You know when you hear chefs talking about “mise en place,” or the process of prepping all your ingredients? Well, that’s what you’re about to do. Cut 1 lemon into wedges and slice off white strip at the point of each wedge, also cutting out seeds (discard white part and seeds). Set wedges aside. Separate leaves of 1 romaine heart and wash/dry if necessary. Tear any large leaves into pieces. Strip oregano leaves from stems; discard stems. Set aside 1 Tbsp. oregano leaves. Finely chop the rest and transfer to a large bowl. Cut 1 cup cherry tomatoes in half.
Finely grate 2 garlic cloves into bowl with chopped oregano. Add 1 tsp. salt, several dashes of hot sauce, and 1 Tbsp. cold water.
Add 1 lb. lamb and use 1 clean hand to knead mixture, simultaneously rotating bowl with your other hand, to incorporate. Knead until a light film forms on side of bowl and mixture holds together in a single mass and is very firm (it will spring back when pressed), about 1 minute.
Heat 3 Tbsp. oil in a large skillet, preferably cast iron, over medium-high until oil is shimmering. Carefully add lamb mixture and press into a single flat layer with a flexible spatula (a fish spatula works great for this).
→ Real Talk: A fish spatula is the only spatula you need.
Cook meat, undisturbed, until underside is browned and crisp around the edges, 5–7 minutes. Watch out for splatter and reduce heat slightly if mixture is splattering a lot.
→ The secret to browning meat so it’s crispy and delicious.
Using spatula, break patty into smaller pieces and turn. Cook pieces on the other side until edges are crisp and meat is cooked through, about 5 minutes.
Remove skillet from heat and transfer lamb to a clean large bowl with spatula, then break up meat into small pieces with end of spatula.
Pour off all but a thin layer of fat from skillet into a small heatproof bowl and reserve. Return skillet to medium heat. Working one or two pitas at a time (depending on size of pitas and skillet), cook pitas until underside is golden and crisp around the edges, 1–2 minutes. You only want to crisp 1 side. Transfer pitas to cutting board crisped side down. Add an extra splash of reserved fat to skillet and repeat with remaining pitas.
Finely grate remaining garlic clove into a small bowl and add ¾ cup yogurt and remaining 1 Tbsp. oil. Season with salt and squeeze 2 or 3 lemon wedges into bowl. Stir with a spoon to combine.
Time to build your gyros: Arrange a layer of lettuce leaves down center of each pita (don’t feel like you have to use all the lettuce). Spoon crispy lamb over lettuce, dividing entire mixture evenly. Top with tomatoes, also dividing evenly. Drizzle yogurt sauce over. Dust with an extra sprinkle of salt, then top with reserved oregano leaves. Add hot sauce to taste and serve with remaining lemon wedges alongside.