68 Chevy Celebrity dies whenever it feels like it

High idle warm may indicate bad coolant temp sensor.

EFI or CARB
we need this fact.
if carb , and you did a tune up.?
then the carb has issues (99% dirty caused) oldest story on earth.
sound to me, the carb is running leak, hot, just like all old dirty carbs do.

If you have a carb its chock .If injection its fuel related filters regulator restrictions if fuel flow ect.

Vapor lock again! Make sure the fuel lines are away from hot surfaces, or insulated.
Also, when it warms up, the automatic choke turns off, and the idle setting has to be set to run at that temp. There will be idle jets, maybe two, and idle stop setting for the linkage.

Low pressure from fuel pump, when the pump is cold the pressure increases, as it warms up the pressure drops (this happens in a pump that is going out) the normal pressure should be at 40 with the key on and engine not running, when started the pressure should stay around 36, any less it won't idle and may run as long as you hold the pedal down. The injectors are opened electronicaly, so as long as there is fuel flow the engine gets fuel to run.So check the fuel pump, soundslike you need a new one

Good chance it is not getting fuel, or enough fuel.
When the rig is cold, the choke is closed. As it warms up, the choke opens.
If the metering jets inside the carb are dirty, they may not be letting enough fuel into the barrels. You could also have a vac leak that is masked by the choke until the engine warms up.

Check fuel filter, gummed up carb. (I think that car still had a carb, if injectors, same issue, injectors could be all gummed up from old gas.)

What can happen, is fuel system can deliver or allow enough fuel to accumulate to start up the car, but it can't sustain the fuel delivery to keep the engine running.

Sounds like you have a vacuum leak somewhere causing the engine to flood.Check all hoses coming fron intake manifold.

reach to the underside of your egr valve and feel to see if the diaphragm moves as it warms up. if not you may need to replace it. be careful not to bur yourself though, the engine and egr can get very hot very quickly

try changing your egr valve first