what is the correct name of the cable that connects the 2 emergency brakes to the main cable? and, if I have the rotors cut, is that the time to replace this cable [mine was cut because it was rusty and my emergency brake locked, 2 days before leaving for the winter ].

 

Not trying to nit-pick but this may help in your search. The brake is referred to as"auxiliary brake" or parking brake.

Try searching through Lexus of South Atlanta pats on on line. You can even call your local Lexus parts. I am not sure if the part would be available as an after-market part. You can try some salvage yards (hopefully from the Southern states).

Salim