I've got a GS 300 and don't have your problem, but my youngest daughter has a Mazda 3 (yes, I know, not a Lexus), but her car started doing the same thing between first and second gears, unless you almost completely let up on the accelerator between shifts. It was under warranty, and we took it in and the dealer said it was a "computer adjustment issue". After being skeptical, I was told (at least on the Mazda) shift patterns are controlled by computer. Whatever the reason, they adjusted the "computer", and it has completely eliminated the problem.
Bottom line, I'd talk to your Lexus dealer. May not have a similar fix, but it costs nothing to ask.