My chevy lumina 3800 series just quits i can be going 60 miles per hr. down the road or i can be stopped and it quit. it will take serveral min. but then it starts back could it be a throttle body sensor or crank sensor or what?

a bad crank sensor will cause car to shut down, and restart in about 10 minutes.while driving down the road.

could be the VSS - vehicle speed sensor .
Speedometer and Odometer
The Vehicle Speed Sensor (VSS) is a gear driven permanent magnet generator. The vehicle transaxle houses the VSS. The VSS generates a sine wave output with a frequency proportional to the vehicle speed.
The Powertrain Control Module (PCM) converts the CKT 389 signal to an output that switches to ground at a frequency of 4000 pulses per mile. The CKT 389 signal drives the speedometer and the odometer. Various other vehicle components use the CKT 389 signal. Refer to Engine Controls.

It appears the cap screws off? It doesn't look like a regular radiator cap. I looked at acdelco parts book.
If the cap is stubborn, cold engine, sometimes I use a pair of pliers with wide jaws, grip the cap and screw it off. I haven't seen your type cap, before. If this was my vehicle, I would certainly want to look in the radiator. I'd get that cap off, one way or the other. Of course, nobody wants to damage anything.

if its been a while change the fuel filter and then have the fuel pressure and volume checked.these symptoms are very common for a fuel pump problem.

sounds like new transmission time. im sorry.

trying to find the oil sending unit is locted.

check fluid level, make sure proper fluid is in transmission otherwise take to trans shop to diagnse if level and type is correct(check at idle normal operating temp)

shuts off while driving down road, then restarts 10 min, later is a bad crank sensor. does it set a fault code, have car scanned, auto zone will do this free of charge.

If the engine revs up while in drive and running at 40mph, your transmission is probably slipping. Try checking your transmission fluid level. If it is OK, I would get it by a garage to have them look at it to cofirm.

There is a recall for valve problems. The warranty for this problem has been extended to 100,000 miles for that. Check with your dealer to see if that is the problem. If no help contact GM.