If the dealership has verified your wheels are correctly balanced on a recently calibrated machine, then you have a front-end alignment issue causing your steering wheel to shake at speed.
The 1998-2003 LX470s for some reason are very susceptible to a toe setting misalignment. Don’t worry as this is easily fixed. Have your dealership’s master tech, and only the master tech, align the front wheels to balance Left and Right sides EXACTLY and to the following specs (all in degrees): Caster, 2.3 (min) and 3.8 (max), 2.0 to 2.3 preferred; Camber, –0.8 (min) to 0.8 (max), 0.0 ideal; Toe, -0.10 (min) to 0.10 (max), 0.00 ideal.
The toe and camber settings are the most critical. While a 0.00-degree toe will reduce your straight ahead tracking slightly, this will all but eliminate the steering wheel shaking at speed. Also, ask the dealership to run an alignment report showing the initial and final settings to verify their work and the alignment to the correct settings.
If this does not solve your problem have the dealership contact Lexus’ regional master tech with this problem, they have heard of this problem at least one time in the past…I had the same issue on my LX and this alignment solved my problem.
Good luck! :)