Combine 1/2 cup pomegranate juice and 1/8 cup balsamic vinegar in a small saucepan and bring to a boil. Reduce heat to low and simmer until the liquid reduces significantly and the sauce begins to thicken, about 10-15 minutes; the sauce is ready when it coats and sticks to a metal spoon.
While the sauce is cooking, mix 4 tbsp pesto sauce with 1 tbsp olive oil, then spread the pesto mixture on both sides of the 8 small lamb rib chops.
When the sauce has reduced, turn off the heat and set it aside to cool; it will thicken further as it cools.
Heat a cast iron grill pan over high heat until very hot. Place the lamb chops on the pan and sear for 2-3 minutes on the first side; flip and sear an additional 3 minutes for medium to medium-well, or 4 minutes for well-done.
Transfer the lamb chops to a serving platter and sprinkle with the pomegranate sauce.