I have a 2006 lincoln navigator, its got a little over 200,000 miles on the clock. It was running fine until we took it to D&J tire to get 2 front tires put on the thing. The guy said we needed an oli change (which admittedly it was needed). Now, we had it last changed it about 12 thousand miles ago (we run very high-end full synthetic oil and always have). Now whenever we come to a stop sometimes it shakes really bad and what you have to do is shift it into neutral and rev the engine to get it to stop. It still does if we put it in neutral at a stop light and do not rev the engine. 5.4Lv8, 6spd automatic transmission, RWD.
I doubt that this is due to the oil change . You mentioned that the oil was changed 12k miles ago. First of all, change the oil more frequently, especially with the high mileage engine you got. If you rev it up to stop shaking, ether your fuel pressure is not adequate while idling or your injectors are dirty. Although these are only guesses and you need to check code(if any) or look into live data.
First off getting an oil change at a tire shop, yikes... Even if you run the high end stuff, oil is still cheaper than an engine,that being said, congrats on 200k miles. Most people can't even make 200k anymore. Since the problem happened after the oil change, I wonder if they accidentally did a bad lol. Wouldn't be the first time I heard of it. Now if that is out of the way then you can check for things like vacuum leaks/o2, sparkplugs and coils and fuel system and the like. Does the car throw any codes? Can help point towards said issue.