Place a strainer or colander over a bowl and line with cheesecloth or a clean kitchen towel. Place yogurt inside and cover. Let sit in the refrigerator for 1 to 2 days.
Blend the mint, lemon peel, and 1/3rd cup of olive oil in a blender. I recommend a small processor such as a Magic Bullet because the quantity is so small.
Taste the herbed oil mixture and season with salt and pepper.
Stir the mixture into the labneh. Season with salt to taste.
Drizzle remaining olive oil on top to serve.