The car will be driving fine and suddenly lose all power and quit. After a minute or two the power returns and the car starts and runs awhile, then dies again

two possibles
coil packs ..
fuel pump pressure to the injector rail

car turns off while driving without warning - 1998-2002 ...

https://www.ifixit.com/.../car+turns+off+while+driving+without+wa...

iFixitwhat would cause my car to turn off while driving & what cause it to start with ... Before you do these, you may consider doing a quick check of your battery terminals. ... So changing out the ignition control module is not a one fix for life job. ... and all thesudden the check engine light would come on and the car would die.

Diagnosing Intermittent Stalling Issues - Underhood Service

www.underhoodservice.com/diagnosing-intermittent-stalling-issues/

Oct 1, 2008 - Replacing a perfectly good ISC motor or solenoid won't fix the ... If the engine stalls while idling or driving, the engine may be running ... The engine may startand idle fine, but run out of power or even stall at highway speeds. ... If the engine is running normally one minute, but suddenly quits, .... Then dies.

Engine Performance Problems Due to Crankshaft Position ...

Going with power lose. Check the grounds. Main three are from the battery to engine, battery to body, and engine to body. I wold check for codes, even if the light is not on. There could be some pending.

have the crank sensor checked also check the fuel system for correct pressure

The choke function is not working on a cold engine.
1 clean throttle body and IAC motor air pathways.
2. Check for engine codes, you are looking for a code that relatws to the wngine temperature sensor.

One possibility is a blocked fuel line or filter. It basically runs out of fuel and you have to wait for it to come through slowly. The other possibility is the ignition system is losing spark as something heats up. You have to wait until it's cooled down before it runs again.

Sounds like you are having a fuel problem with the fuel filter. If you have not had your car serviced in quite awhile i would do so. At least change the fuel filter and check the air filter as well. Hope thias will help you.

if not the fuel pump, maybe an ignition system component is failing after it heats up. I'd check if fuel present, then diagnose ignition.

Quite a few things can cause a car to die after idling for awhile, but if you have verified that the fuel pressure is actually dropping when the motor dies, the likely culprits are:
1) Electric fuel pump in the gas tank is bad
2) The fuel pressure regulator (on the throttle body) is bad
3) An electrical problem in the power to the fuel pump (like a bad fuel pump relay or lose ground wire to the relay's circuit)

Man! Lexus is ****! I have the same problem.