I did this service last Sunday (Oct 25th, 2020). I ordered he following things from Amazon to get it done:
12 qts Toyota brand WS AT Fluid
https://www.amazon.com/gp/product/B0799J7D5M/ref=ppx_yo_dt_b_asin_title_o01_s01?ie=UTF8&psc=1
The ODB Software and an ODB cable for Toyota / Lexus the young lady used in the video
https://www.amazon.com/gp/product/B07BCL3DFR/ref=ppx_yo_dt_b_asin_title_o01_s00?ie=UTF8&psc=1
This same pump the young lady used in the video
https://www.amazon.com/gp/product/B00I6BG1KI/ref=ppx_yo_dt_b_asin_title_o00_s01?ie=UTF8&psc=1
As well as a couple of pitchers so I could drain old fluid in one, and fill the other up to the same level to pump back in.
Once I was done with the service, I took it for a test drive and it was STILL making the loud grumbling / vibration at around the ~1200 RPM mark between 40-60 MPH. I immediately decided that I would just go ahead and let my mechanic install a used transmission in the vehicle, so Monday morning I drove it to him and told him to find a transmission for me and give me an official price quote, because up to this point he was giving me ballpark numbers. The mechanic is maybe 20 miles from my house, and I specifically remember that right before I pulled up to his location the car made the grumbling / vibration again.
He kept the car 4 days, but didn't do anything to it, and called me back saying he had not located a transmission yet, and that I could pick up the car because it could be awhile before he found one, and needed to make room for other cars at the shop. I went and picked it up Friday Oct 30th. It made the sound once more after leaving his shop, before getting on the highway to make my 50 mile drive to work, and it has never made the sound again.
Honestly, the car drives great now. Now that the drain and fill is done, driving down the road is noticeably smoother at ANY speed and RPM, not just the speeds where it was grumbling and making that loud reverb noise. Since friday I have put probably 500 miles on the car (def filled it up with gas twice) and I assure you the sound is gone. I highly recommend you get this done. I may have said this before, but I basically had ZERO faith that any shop would have done this right other than me, so I did it myself at home. I actually have quite a bit of tools, floor jacks, and jack stands at my house in my garage so I was very comfortable giving it a shot because if I somehow screwed up, I already decided I was buying another transmission anyway.
If you are taking it to a mechanic, maybe show them the video I posted so they know what it is you want done. Maybe even tell them you will provide the transmission fluid yourself.
Looking around the other forums I learned a couple of things about the transmission.
1: Nobody suggests that you do an actual transmission FLUSH. They all say flush is a no-no, and you should instead drain and fill like the young lady in the video. Most people say do at least 3 cycles. I ordered 12 quarts and just kept doing the drain and fills until I used all my new fluid, which in my case was 4 drain and fills. Between each fill I would get in the car and cycle through the gears 3-5 times just like the woman did in the video.
2: Lexus USA is apparently the ONLY country where Lexus says that transmission fluid NEVER needs to be changed. Japan, Europe, and even Canada have a suggested maintenance schedule of 30,000km or something like that where you need to get the fluid changed out. This is just what I read other places online, so feel free to do your own research on that.
Having said that, I would bet my bottom dollar that the transmission drain and fill procedure shown in the video will get your problem taken care of. I plan on doing this service at least once every other year, but possibly once a year. I would love to find a mechanic that would do it for around $200 labor if I provided all the materials. I don't enjoy working on cars, and am honestly not very good at it, but was still able to knock this out.
And just to reiterate, my problem was specifically my car would have a very loud rumbling / shutter / vibration during city driving whenever the car was in maybe 3rd or 4th gear (I cant tell which gear but this is my best guess) and the RPMs were somewhere between 1000 ~ 1300RPM, usually this would put me between 40-50 MPH. The car was ALREADY doing this when I bought it a month ago, and the previous owner said he owned the car for a year himself, and it made the sound the whole time he had it as well (maybe he's lying, IDK). The sound was VERY noticeable, and occurred often, but other than this specific issue the car ran fine, shifted gears fine, and accelerated fine. No check engine lights or anything like that..I ALSO took it to the Lexus dealership in Clear Lake, and they told me I needed a new transmission and torque converter. LOL
Now the sound /shudder / vibration is 100% gone and the car overall drives much better. I mean, I thought it drove fine before except for the noise, but now I see that I was wrong and can tell the difference. No new trans, no new torque converter. Just changed out the freaking transmission oil and voila !
Sorry for the wordy response.
I will do my best to keep an eye out on this post for any questions you may have as a follow-up, but I feel like I gave you all the info I have. Rest assured that if the sound comes back, or if I have any more updates on this I will definitely come back to post, because I do not want to leave anyone hanging with half- way answers or mislead them. I was pretty stressed out about this damn sound, and was pretty disappointed that nobody followed up their posts with answers, so I wont do the same, and hopefully this helps someone in the future.