Firstly I had the same issue and yes it is that little bit in the motor. I figured something out today though. A non invasive check before removing the manifold. If the arm circled in the back swings left to right, then yes that gear is loose. After the fix this arm has no play.

Sits right behind the coolant cap

 

did u find the problem

 

Yes we did, It's based on that link with the quoted below, my post shows the picture that could help confirm your issue without taking any parts out

Just registered to add how I fixed my P2009 on a 2009 IS250. This was the 1st post I could find so hopefully that helps somebody else with the same issue.

Took apart the upper plastic intake manifold and lower aluminium intake manifold to reach the motor on the right side of the lower intake (when viewed from the front, it's the driver's side in the US). Removed 2 screws (they were on real tight) on the actuator flap motor and found a nut in there loose and flopping around. Put 2 drops of blue Loctite and fastened the nut. The original idea of this fix was found here.

https://www.drive2.ru/l/451038637363037292/

Had to disconnect a bunch of harnesses and remove the throttle body to get in there. Hopefully, that fixes my problem.

 

Look back at Faheem picture in this post. In the middle of the engine of the car, right past the radiator, there is this lever. It appears to be like a choke lever, but it's not. If this goes back and forth even with some resistance, here lies your problem!! But unfortunately, it's not the lever that's bad, this lever has a bar that partially opens butterfly's within the intake manifold itself. On the other end (still middle of motor, just towards the back of engine) is a actuator or small gear box, maybe about the size of a coffee cup, attached by 2 large Phillips Screw. There is a nut that loosen's itself over time, inside that actuator housing. I put a lock washer and some blue loctite and tightened. Put back together, and VSC warning and check engine light all went off immediately, after I put back together.
This job will take several hours. All of the plastic, and the huge throttle plastic assembly will need to come off, directly on top of the engine. I will note, this is a great time to change spark plugs, because you will expose all of this in your tear down. After plastic exposed, then take off the 4 nuts/ 4 bolts holding the aluminum intake manifold. Once you have intake manifold in hand, take to work bench. Tap on the 2 large screws, to loosen. Unscrew and nut should fall out. Put nut on, put back together and you're done. I use different colors of fingernail polish overall during teardown and put a Dot on, connector's/vacuum hoses, nuts/bolts, etc so I remember how to put back together.

 

I did this already before it was posted by another member who was having similar issues. Someone in Russia I think was the one who solved this issue first. I found this link by searching the same topic. I'd say if you're mechanically inclined. Especially if you have a IS250. While doing the spark plugs do this. It will eventually come loose. I'm sure in a few years will see this post come up more often.

Here's another one for referenreferences recently.
https://www.clublexus.com/forums/is-...-solution.html

Russian link:
https://www.drive2.ru/l/451038637363037292/