Engine keeps shutting off

Hello, which code number are you getting? Lexus calls the cam sensors- VVT sensors. Which stands for variable valve timing. The B cam sensor which is labeled vv2+ on the wiring diagram is a 2 wire sensor. And a high input code means the sensor is shorted to its reference voltage (which is one of it's 2 wires, the sensor itself is shorted internally or the signal wire is shorted to a power wire. Can you give me the exact code number, it should be p0016 or p0011.

Yes, actually this car has 4 cam/VVT sensors. The ECM reads cam timing off of the VVT sensors, so sensor B I'm assuming is going to be on bank 2. Can you give me the code number that you got from your scantool? You can check all 4 if you want to. But the code may give us some better direction. All the powers, grounds and signals all go back to the ECM. So it could be a bad sensor or one of the wires is losing ground which usually causes a high voltage reading from the sensor.
Here are some extra information about how the cam timing works, there are sensors on both intake and exhaust camshafts.

Yes, it definitely could be the problem, the engine computer uses these inputs for injector timing. I did some research last night on this code, it applies to the bank 1 exhaust cam sensor. It could be that the exhaust camshaft timing is off, since the timing chains or belt have to come off to replace the cylinder head, the timing chain could be off on the exhaust camshaft. This will throw everything else off. If this started happening right after the head was replaced, then something was installed wrong. The cam phasers need to be timed exactly right on. Here's the detecting conditions for that code. You may want to bring it back to the place that did the work and have them fix it. Special tools are required to hold the camshafts in place while setting the timing. I'm adding a picture of the wiring diagram for the cam and crank sensors.

I hope this helps you. When it comes to variable valve timing and the cam phasers, everything must be locked in the correct position, cams, crankshaft. It's not an easy job, and everything must be lined up perfectly.

Is there something else going on with it? Did you want the timing belt? Just in case you wanted these. I did some research last night and what's happening is the system is going into fail safe mode and shutting the engine off is one of it's options.

Replacing the idler pulley solved the p0368 code? The only possibility is that when changing the idler pulley is that the wiring for the cam sensor b got moved and is now making a good connection.

That code is still a serious code. How is it running at this point? Besides the shutting down.

You're going to have to check that sensor, it's definitely going to effect performance. It's a 3 wire sensor, so it will have a power, ground and signal wire going back to the PCM. It may be a wiring issue, or the sensor is shorted out internally. It's going to on bank 1, which is the side of the engine that cylinder#1 is on the exhaust camshaft (which will be facing the exhaust manifold). Check the plug and wiring for any corrosion or broken wires.