2001 Mustang Conv. 3.8L sputtering sound????

I'm not exactly sure but sputtering in my experience has been spark plugs, fuel filter, and have you done a serious Seafoaming treatment lately?
Otherwise, it almost sounds like you want to describe a steering mechanism failure or bearing issue of some kind, maybe ball-joint, or lastly transmission.
Performing the 3 PM items I mentioned first should be done to help eliminate anyone second guessing while diagnosing.

The lean code may be related to the cat converter , but atm, not sure.

This sputtering sound, it would be helpful, can you describe this sound any better? Can you tell where the sound is coming from? Is it an exhaust noise? Can you smell anything? Perhaps I was thinking it MAY be an exhaust leak up front, but I can't be sure until I get more info.

The Traction Control problem you speak of.. does not sound like a problem at all. Let me explain something here..... The whole purpose of traction control is to limit the amount of engine power applied to the rear wheels when the wheels appear to move uncontrollably ... that is, ONLY when the traction control system detects the wheels are randomly moving at odd speeds and jerking around creating a slop condition, such as the wheels starting to slip in gravel or snow. When the wheels start to slip, the Traction system reduces power from the engine to the rear wheels until they stop spinning or slipping over the surface. This is what you are considering as an almost stall condition , This is normal and it will NOT stall the engine. You can however, turn off the Traction Control , simply by pressing that Trac Lok/contol button. Once you press it, a light on your dashboard should turn on and stay lit. TL will turn back on once you shut the car off. SO you will have to press the button again later to disable it, Only do this if you are looking to do a burnout or the T lok system is actually preventing you from getting out of a tight spot...... which is RARE! This T lok actually works and has a life saving usage, You are only seeing this light because the cars computer is engaging T-lok and it momentarily flashes that light on the dash when that happens. This is normal.