I went to remove a wheel today and found a problem. One of the lug nuts, not the lock one, feels loose and like it has a plastic cover over it. The lug wrench and a 3/4" socket will not fit over it and yet a 13/16" socket is too loose. I can wiggle it with my fingers but I can't pull it off with pliers or pry it out with a screwdriver. What is it and how do I remove it? Thanks.
BTW, my spare was flat so that is a good thing to check once in a while.

 

The fasteners are metric not fractional. Have you tried a 19mm 6-point socket?

The outside cover should turn with the lug nut, but sometimes becomes damaged if an impact socket has been used to tighten the wheel nuts.

 

I don't have a hex 19 mm but the 'star' 19 mm does not go on. (Nineteen mm is 0.748" so pretty close to 3/4".) Since the socket won't go over it, it must be damaged. How would I get it off? I don't have a 20 mm socket. Buy one?

 

Purchase a 19mm 6-point socket.

All fasteners on the X760 are metric and can be damaged if fractional tools are used to remove or install them.

 

Just to finish off my post...
I was "practicing" removing the wheel at home in case I had a flat on the road. I had never tried jacking the car and we have some desolate stretches where it might be better to change it than to wait for help. I used the lug wrench that Jaguar supplies since I don't normally carry many tools with me. I have a feeling that I spun the cover and ruined it since the wheels have never been removed before by anyone else (10K miles). I probably should not have used their lug wrench but I am an optimist and thought it would work! I am posting this in case anyone else finds themself on the road with a flat. Maybe this will save someone some grief.

 

I suspect that (even in Arizona) there may have been some rust on the lugnut threads after 10,000 miles, making it more difficult to turn the lugnuts, especially with the supplied wrench which does not offer a lot of leverage. Here in the rainy UK, rust on lugnuts (wheel nuts here) and the studs is always a problem, together with corrosion between the alloy wheels and the steel hubs. When I get a new to me car I always have the wheels off and use a smear of copper grease on the studs and the hub surface. You'll probably see advice not to do this because of the supposed risk that grease may cause the lugnuts to come loose, but in some 40 years of motoring I have never had this happen to me.
As for coping with the loose lugnut cover, you may have to get a socket that just too small to fit and hammer it onto the lugnut deforming the cover in the process. Then of course you'll need a new lugnut and I think Jaguar only sell them in sets of 4 or 5!