Is the lambda sensor still necessary after a mapped ng

After a mapping is complete and the car is running fine, is the lambda sensor still important or can it be disconnected and the car will still run as per the map?

It's not strictly required. But it depends on the quality and completeness of the tune.

Is it air temp correction fully tuned, particularly at WOT? Will it still run right at any elevation? Is the tune accurate during warm up? Is the injector data correct?

It's not ideal to rely on EGO correction to fix any of these things. But plenty of 'tuned' cars just have the VE table tuned, and everything else is just the default values in the ecu. So it works under the condition when it was tuned, but change any variables and it's not so good.

But yes, a proper and fully tuned ecu should be able to run at or very near the lambda target, without using any wideband correction.

As Matt said, you've tuned to those very specific conditions - equipment (parts' condition, engine temperatures, etc) and ambient (air pressure and temperature). These will change over time with wear and weather, so the 'correct' tune and what you have will tend to separate over time - with the lambda there is usually some proviso for the ECU to self-correct, at least partially, for this which should hold it closer to the tune the engine works best on for longer.

The lambda, if you have a display, may also help indicate developing problems.