Squeeze the juice of half the lemon in food processor. Set aside the other half of the lemon for cooking with the chicken. To optimize the amount of juice that you can squeeze from the lemon, roll it back and forth a few times under the palm of your hand to get the juices flowing.
Crush the garlic by placing the whole unpeeled clove under the flat side of a large wide knife and, using the palm of your hand, press the blade down on the clove, crushing it and splitting the skin. Peel the garlic, discarding the skin, and add that to the processor.
Add the chopped cilantro and peanuts to the food processor and chop until all ingredients are combined.
With the food processor on, slowly drizzle in the avocado oil until combined.
Pour over chicken and rub under the skin of the chicken, add slices of the lemon around and bake uncovered for 1 hour at 375 degrees.