Preheat the oven to 400 degrees. Prick the eggplants several times with a fork and place them on a baking sheet. Roast for 35 minutes until soft. Let them cool slightly, then scoop the flesh into a food processor.
Add two garlic cloves, two tablespoons of olive oil, lemon juice, and a pinch of salt to the food processor. Blend until smooth. Set the puree aside and keep it warm.
Finely chop the olives, capers, remaining two garlic cloves, and parsley. Mix them in a bowl with the remaining two tablespoons of olive oil to make the tapenade. Season with a little black pepper.
Pat the lamb chops dry and season both sides with salt and pepper. Heat a large skillet over medium-high heat. Add a light coat of oil if needed. Sear the chops for three to four minutes per side for medium-rare. Remove from heat and let them rest for five minutes.
Spoon the eggplant puree onto plates. Place two lamb chops on each plate and top with a spoonful of olive tapenade.