Will start and run perfect for 20ish miles, until warm. Then it will drop power for seconds and kick back in. Reminds me of golf cart with throttle governor...
does the constantly. Will accelerate but when level out it drops fuel or spark over and over . Once this starts, engine hot, it idles rough ...
Mechanics have said it's a cam timing issue, it's a bad computer, it's a throttle sensor, it's a mfs, .
Can anyone help me with the root problem?

What would be helpful is what OBD code the mechanics pulled from the vehicle to come to that conclusion.

Codes are 420, based on charcoal canister and a VVT code.

Seems like VVTi is preventing right amount of power.

Salim

OK... I'm not an auto mechanic so can you elaborate on the fix, please?

With the information provided I wouldn't venture a fix. So far you've written:

1. Engine loses power when warm
2. Codes are 420, based on charcoal canister and a VVT code.

The first is vague and could be caused by multiple things. You might even be describing "limp mode", which the car goes into when some codes are thrown. It's hard to tell.
The second doesn't make any sense. Code P0420 is "Catalyst system efficiency". Likely causes of this are a leaking exhaust, a bad catalytic converter, or a bad oxygen sensor. No idea what "based on charcoal canister and a VVT code" means.

An issue like this needs accurate information and a proper diagnosis or you could end up unnecessarily changing lots of expensive parts.

Observations zeros in to a potential cause of trouble. next is confirming a failing part.

Max has pointed out that first determine if you are in limp mode which is can limit the power yet again.

If it is indeed vvti then a cleaning or replacing the valve can cure your problem but then a true diagnosis is still needed [typically special tools and equipment]. Without it your effort would be a shot in the dark.

Salim

As stated, I had a local mechanic look at the issue, with scanner. He didn't pin point a cause , just vague possibilities.
I have scheduled an appointment with a local, reputable import auto shop. But they're booked 2 weeks out. Was hoping someone here had experienced this problem and could direct me to a replacement part, sensor, solenoid, etc .
Thank you all for your input.

What is the RPM and the highest speed you can get to [Do not exceed 4.5k rpm]?

You are welcome to throw a part(s) and see. VVTI solenoid. Will it fix your problem ... no guarantee.

I'm repeating what the local mechanic told me about the 420 code. The two issues are not related. The VVT code is a result of the power skip problem , I'm told.
Also, according to scanner, vehicle is not shifting into 4th gear.

When some codes are thrown the ECU will go into fail-safe mode. When in fail-safe mode it will run rough and not go into 4th gear.

Thank you for the info.
Makes sense as when mechanic cleared codes it ran normal for a bit..

OK. The usual approach here would be to clear the codes and then see which code is reported first. Other codes may be caused by the first one.
In the event there are multiple codes reported at once there is a troubleshooting order.

Consider buying a code reader so you can read and clear codes yourself. You can also go to your local Advance Auto or equivalent where they will read them for free.

I'm not sure of RPM... It accelerates no problem, hitting 70 mph on highway. Trouble presents when holding a consistent speed.

My appointment with Cabarrus Imports Auto Repair shop was Tuesday. Had to schedule a week out . Delivered Lexus at 9am. , Was repaired and ready for pick up at noon. Problem was VVT solenoid valve on second bank. Bill was $126.00.
Lexus runs perfect .