Combine the mayo, garlic, lemon juice, and a pinch of salt in a small dish. Set aside until ready to serve (in the fridge if you make this well in advance).
Toast or broil the burger buns lightly.
Preheat a large skillet to medium-high heat with a drizzle of oil. Preheat the broiler to high. In a bowl, mix the turkey meat, onion powder, chili powder, cayenne pepper, and generous amounts of salt and pepper with your hands. Form into 2 patties.
When the oil in the skillet shimmers (usually about the time you've finished making the patties), add the burgers and cook for 5-7 minutes on each side until cooked through. Top with the cheese and broil for 1-2 minutes until the cheese.
Assemble the burgers: spread garlic mayo on both sides of the bun. Add sliced onion and lettuce, top with a burger, and serve!