Most likely a problem with the carburetor.
fuel filter? fuel lines? what all have you checked.
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.
Low fuel pressure
A plugged up fuel filter, a faulty fuel pressure regulator or a faulty fuel pump.
Plugged fuel, air filter, or catalytic converter can cause that.
A faulty crank sensor would cause no spark and no fuel.
I would suspect fuel pump failure.
Fuel pressure regulator.
I had same problem -- fuel pump went out.
Chevy trucks did not use a RESET switch on there fuel pumps. You either have a bad fuel pump relay are fuse, It may be that the fuel pump has just quite. You did not say what year it was and I do no that Chevy had a problem with the wireing harness / connecter on the top of the fuel tank that would cause the pump to quite.
There are several things that can cause your 1998 Chevy to randomly die out. The most common cause is a malfunctioning fuel pump.
Low fuel pressure, stoped up fuel filter.