I also broke OEM security lug nut on solara few years back.
I could not get one of the security lug nut lose possibly because a shop I did saftly inspection has over tighten it.
I broke about 1/3 of the key in process. I tried to take the nut off with broken key again and again, then I even broke part of the nut.
I ordered replacement key, and tried again. I broke the key again.
Took it to the shop I did saftly inspection. They suggested taking it to a dealer and have them cut the wheel off. (Really?

)
Did some google search and found that I could just use a socket slightly smaller than the security lug nut.
So, I just purchased 12 point socket (6 socket may not have enough grip) sligtly smaller than the security lug nut and hammered it on to the security lug nut and removed them.
I got so frustrated with these security lug nuts, I replaced all 4 security lug nuts with regular lug nuts.
Hopfully no one will find OEM wheels worth robbing.
