I have a similar problem with my 1993 ES300. The odometer does not display. Some of the information I have found indicates it may be a failed battery backup for the odometer (in order to retain odometer/trip odometer information when the car is shut off). In any event, it seems that the instrument cluster will need to be removed in order to determine the exact nature of the problem. The local Toyota dealership quoted me ca. $450 to repair, assuming it is something they can fix.
If you search for "lexus, es300, instrument, display," you may find some information about removing the display. The Haynes manual for 1992-1996 Camry has comparable info.