My 2000 RX300 with 160,000 miles shifts very slowly from 3 to 4. I let up on the gas when this happens. Had a Tech look at it while I was on vacation, he said it was a dirty Mass Air Flow sensor (that's the one by the air cleaner). He cleaned it and It worked perfect for a month and a half. I was so happy that it was a easy thing to fix. Then it started again and I cleaned it and work for awhile, after that it didn't help, so I replaced it. That didn't help. Had the #2 knock sensor replaced to the tune of $800. No help. Once it gets to 4th everything is OK. Can anyone HELP, PLEASE?

If anyone else is having this problem, try cleaning your Mass Air Flow Sensor.
Hopefully it will work for you.

 

You should probably start with changing the filter on the transmission. And get the engine codes read if any are present. I know when certain sensors go, they stop the car from entering 4th gear.