I believe that you are describing some sort of "torque converter issue". I have absolutely no basis for this statement, but I believe that this could be caused by the main computer module(ECM). If you plan to keep the car, save yourself a lot of headache, and look into having the ECM repaired.
https://siaelec.com/product/lexus-ls...repair-return/
It's cheap, but you'll be without the car during the process.
For whatever reason, something seems to get weird with these computers at some point, and mysteries develop. ...Leaky capacitors? It's definitely voltage related, and you can do a number of "voltage related" things to create temporary satisfaction, but it's always temporary.
I wasn't able to keep my LS. A huge regret indeed. Knowing what I know now, however, I should have STARTED with that ECM rebuild.

 

Oftentimes cold solder joints develop at the circuit board bulkhead connectors.
The electronics industry transitioned to low-lead/no lead solder..and it is not as durable...

The LS400 Engine ECU is located on interior side of firewall, while LS430 mounts the ECU in the hot engine bay...probably to save a few pounds of copper.

I recall my 1982 Mercedes mounted the ECU and battery on engine bay firewall, but employed a generous fixed barrier to shield from engine heat....(never had to replace the battery)

The more intense underhood thermally cycling - expansion/contraction of circuit board and connectors, increases likelihood of compromised solder joints.

 

THIS. This is all very real. I'm obviously not sure exactly what they go after with the repair, but the fact that they offer a repair at all would validate your statement. It really SEEMED like leaky caps in my case, but crap solder is possibility #1-B in my mind.

 

Adding my 2 cents in here. I just had the TSB done at a Toyota dealer and the difference is fantastic. I am thinking I do not need to bother with the ECM repair now. The car feels new-car smooth. If your LS has not had this done yet, get it in there.

 

Does anyone have a copy of TSIB No. SS001-01 "ECU Flash Reprogramming Process" ? It is specified in TC006-04 under "flash reprogram ECM" step 2. Thanks.

edit: answering my own question. Here it is: http://media.fixed-ops.com/lex_servi...s/ss001l01.pdf