If at 57k miles your transmission went bad and the invoice at that time had these comments:
"Lexus Reman Transmision defective, Replaced Transmission Assembly. "
I read that as saying the "Lexus Remanufactured Transmission is defective, transmission assembly has been replaced" to me that means the transmission that was defective at 57k miles was a remanufactured transmission, meaning the original transmission was replaced with a remanufactured one at some point before you purchased it...
I would go to a separate dealership and have them pull the history for the vehicle. Something doesn't add up here, why would they call the transmission you had replaced at 57k miles a "Remanufactured" transmission if it was the original transmission?
Nothing wrong with a remanufactured transmission, but something doesn't seem right about your situation, we have this weird reference in your original replacement to the one being replaced being "remanufactured" and now you need another transmission 30k miles later. There's something they aren't telling you IMHO...