Peel and rinse the large outer leaves from a head of lettuce (these are the largest). Set aside.
Divide the meat into 8 sections, each patty will be 2 ounces. Press into burger shapes between your hands. Add to a small amount of cooking fat in a hot skillet over med-high heat. Wait for the oil to be super hot before adding the meat. Flip burgers after a minute or two, once the first side becomes crispy. Cook the second side until done to your liking.
If you want to make cheeseburgers, add the piece of cheese while the second side cooks. Cover with a lid until it melts.
While the burgers cook, mix all the ingredients for the sauce. Finely chop the dill, juice the lemon, mince garlic, and mix into the yogurt. Season with salt and pepper. Stir well to combine.
To assemble, arrange the patties on a piece of lettuce toward the bottom part that attaches to the stem. Top with pickle relish, tomato slices, and grilled or sautéed onions (all optional). Pour a few spoons of sauce over it all.
Wrap up the contents with the lettuce, tuck the side ends in first, then roll down the top to close. Double up with a second piece of lettuce if needed.