"If true, this means that everything that Einstein sold is a complete lie."

That's not factually correct.

You see, that there is my biggest problem. It is factually correct.

The premise of the "Theory of Relativity" is that to all observers the speed of light is constant.
Thus, you can only approach the speed of light.

So, if an experiment shows that the speed of light can be broken, then the theory has been debunked.

Further, if the measured speed of light changes, the theory is also debunked.

(This is why the metereologists got together and FIXED the speed of light. Because it wasn't supposed to be changing. Because the theory of relativity said it is a constant.)

So, there you go, two disproofs of Relativity, but Relativity still stands.
So much for an "an easily falsifiable theory".

There are many more disproofs.
But most of them would involve NASA admitting they do not use relativity.
You know, the lie keepers admitting that they lie.