Only a general answer here: the vehicle doesn't want to idle coming down from power. It's probably a fuel or a "tune up" problem, meaning things aren't adjusted properly anymore. The fuel pressure my be dipping due to an old fuel filter or a fuel pump pump or fuel pressure regulator problem, but we can't tell. It is also possible that there is a problem with the ignition electrical system, but that is unlikely. See the related question and do an advanced search. There are many other similar questions in WikiAnswers addressing this issue. It is not unique to your make and model of vehicle.
I had that issue with my Cavalier and it turned out to be a fuel pump problem. I would check with your local mechanic.
Low fuel pressure
a vac leak
There are many things that would cause a 1999 Chevy Lumina to stall. The car could be too low on fuel, have a leak in the fuel line, or an old fuel pump or filter.
its probably a computer issue or an electrical issue some where in the car i had the same problem with my car and it was computer
have you checked your fuses?
I would suspect fuel pump failure.
i would like to remove the backseat from my 1992 chevy cavalier
Bad heater core.
Dead battery
Blown Head Gasket or Bad Cylinder Head
You need to check all of the mounts. Get a manual to show you where they are.