I own a used ‘certified’ Lexus SC430. It has had a shimmy in the steering wheel when I accelerate between 67-72MPH since purchase. Lexus first told me it was the top being down, then they told me it was the run flat tires (something about them not being perfectly round even though they were new when I bought the car), and - after I got new tires - they replaced a wheel. Now, the shimmy is present at about 43-45MPH and worse at the 67-72MPH point. Lexus is throwing their hands up. Any ideas?
What year Lexus?
My guess is a worn suspension part. Was/is there any kind of warranty on the car? If so read it very carefully.
I have a 2003. I purchased it in 2008 as a certified ‘pre-owned’ car from the local dealer. If it’s suspension, why would I only feel it at certain speeds?
Is it about speed, or is it about acceleration? You’ll want to get that straight. So get it to the speed ranges that you know are problematic and accelerate at least moderately if not hard. Then just kick off the gas - does the shimmy change when you kick off the gas? If you have a place to do it safely you can also briefly shift it to neutral with no foot on gas to completely coast anywhere in the right speed range. What happens?
Figure that out and report back.
There are lots of reasons that different problems only show up at certain speeds.
There are also lots of mechanics in the world. Perhaps you could get another shop to look at it?