I owned a 90 LS 400 for about 8 years, finally gave up at 380,000 miles. The radio did the same thing to me that happened to you, My garage- a guy I trust a lot, told me the radio was bad and ordered one from Lexus (you can only get a refurbished one from Lexus) at a cost of $615.00.
you can check the radio connections by first removing the ash tray and oppping out the ashtray hold. This is held to the dash by fingers that go into the dash/ YOu cannot hurt it by pulling it out and it takes a little force to do. Then you can get the radio out by doing the same thing to the radio, All of the wires to the radio are plug in connectors and cannot be confused, try to get a better connnection by pushing them in. It didn't work with mine, but who knows, maybe you will be lucky.