I had the same problem, as Lexus didn't have a receiver available when I bought mine.
I found out that Lexus had a wiring harness available part no.08942-48870-BB, sells for about $48, but it's the one that fits the special socket, and includes the trailer socket and a mounting bracket.
Until I made a fuss, the dealer told me you could not buy the harness, then they admitted it could be speciel ordered.