Begin by reducing the pomegranate juice. Place cold juice and corn starch in a small saucepan, and whisk until blended. Put over heat and, stirring constantly, cook until it reduces in half and makes a syrup-like consistency. Remove from heat and allow to cool completely. Divide into two small bowls.
Cut figs into small dice. Combine in a bowl with pomegranate seeds, jalapeno, onion, and cilantro. Add lime juice, a splash of olive oil and some balsamic vinegar. Stir well to combine. Add a few tablespoons of the reduced pomegranate juice to the salsa. Season to taste with salt and pepper. Then set aside. Reserve remaining syrup.
Pat lamb loin chops dry on both sides. Using a brush, coat each chop with pomegranate syrup (from 2nd small bowl. Discard leftover syrup from this batch). Season with your favorite herb-forward rub and set aside.
Preheat grill to high temperature.
When grill is hot, cook chops for about 5 minutes per side. Internal temperature should be 130° for medium rare.
Allow chops to rest 5-10 minutes, then serve with pomegranate and fig salsa and a drizzle of additional pomegranate syrup.