I purchased a 2013 GS 350 in September 2013. Within a few weeks I noticed a hesitation when accelerating from a dead stop. I immediately notified the Lexus Dealer. They told me they had no other similar complaints. I went on line and found a few Lexus owners with the same problem. These owners describe exactly what I was experiencing. Well, after one year I think the problem is solved. A few years back Toyota/Lexus had a problem with floor mats sliding up on the accelerator pedal and causing unintended acceleration. When the brakes were applied, the car kept accelerating. To solve the problem, Toyota/Lexus introduced Smart Stop Technology (Brake Override System). A sensor was installed that monitors the brake pedal. When the brake and gas are applied together, the computer software tells the care engine to stop or basically decelerate. This can create a dangerous situation when making a left turn into oncoming traffic or someone behind you will not see your brake lights on and could run into you. This has happened to me but fortunately no one has hit me but came close.
So, if you are a driver that uses two feet, another words brake with your left foot and right foot on the accelerator, guess what happens. The care will hesitate if you have one foot on the brake and one on the gas. You only need to lightly have your foot on the brake and not even pressing down that hard. In fact if you just rest your left foot on the brake pedal and step on the gas with your right foot, you may experience this hesitation.
I was one of those two foot drivers. I used both feet on my previous car, which was an Infiniti, but it must not have been equipped with this Smart Stop Feature, so I never experienced any hesitation.
I stopped using two feet and so far my car has not hesitated. It's been more than two weeks and I have not experienced any hesitation.
CONCLUSION: If you use both feet to drive and experience any hesitation when accelerating, do not use two feet to drive and your hesitation problems will stop.