Can lamb chops be light fried\sauteed to fully done and how long does it take?
If you're aiming for fully done, it may be best to not try to cook too fast. If you use high heat, and your chops are reasonably thick, then by the time the center is fully done, the outside will be overcooked. High heat and thick cuts works much better when you're aiming for, say, medium rare, so that you aren't trying to heat the center as much and thus don't need to overcook the outside as much to get it there. (Maybe this is why you thought pan-cooking was for thin cuts only?)

You can avoid this by cooking on lower heat for a longer period, possibly even adding a bit of liquid and covering so that it braises/steams and heats from all sides, not just the bottom. Then, if you also wanted the browning from cooking on high heat, you can increase the heat briefly at the end. (If you used water, make sure it's all cooked off or that won't work.)

Overall, the time to cook will depend on the thickness. It might generally be faster in a pan than broiling (UK grilling) because the meat's in direct contact with a hot pan, so there's faster heat transfer. But specifics of course depend on how close you're getting to the element when broiling and how hot you have your pan.