I have a 2010 LR 2 and have just purchased a winter wheel tire package from tire rack. I do the change over myself on my other 2 cars. I thought the socket size was 21 mm and the new lug nuts are 21mm. But the 21 mm does not fit the other nuts and a 22 mm Is too big so I can’t get the old tires off. Any suggestions? I’ve always had a tire shop do a winter tire change over with just the tires but I was trying to avoid that hence the tire package

 

Try a SAE socket 13/16 or 7/8

 

A 13/16 didn't fit and the 7/8 did but the only 7/8 socket I have is a 12 point and it starts to round off the nut. I'm going to get a 6 point and see if this works. I tried using the oem lug wrench but I can't get that on the nuts. We are soon heading to Nantucket and we'll be on the beach; a few years ago the rover got a flat on the beach and I was able to change the tire with the oem lug wrench. I'm now trying to sort this out just in case there is a problem (as well as the changeover)

 

Probably the covers on the lugs have expanded due to the wrong size socket being used or corrosion.

 

I have the same problem with the lug nuts on the spare tire on my D2. They look good, not rounded or damaged, but nothing standard or metric, 6 or 12 point I've tried will fit. They're asking for a fire wrench next.
Fortunately a socket fits the lugnuts on the wheels on the truck just fine.