Welcome to the forum.

There is no yes or no answer to that. It is possible to get permission to enter the golf club and drive to the lighthouse. Perhaps lunching at the resort would allow admittance? However, you cannot just drive in. There is a big gate that is manned to only let select people through. I suppose they want to keep it "exclusive" for big shots with lots of money. I suggest you make your arrangements in advance if this is important. Just driving up to the gate and trying to talk your way in may not work.

There are also other lighthouses in Ireland you can visit if you can't get in to Old Head.