Add pomegranate juice and balsamic vinegar to a small saucepan and bring to a boil. Reduce the heat to low and keep cooking the sauce until it evaporates a lot and starts to thicken (about 10-15 minutes). You will know that the sauce is ready when you touch the sauce with a metal spoon and it sticks to the spoon.
While the sauce is cooking, combine pesto sauce with olive oil. Spread the pesto on both sides of the lamb chops.
The sauce should be ready by now. Turn off the heat and set it aside to cool down. It will thicken more, once cooled.
Heat up a cast iron grill pan on high heat. When the grill pan gets hot, place the lamb chops on the pan and sear for about 2-3 minutes. Flip them over and sear for 3 more minutes for medium or medium-well and for 4 minutes for well-done.
Transfer the lamb chops onto a serving platter and sprinkle with pomegranate sauce.