About Lorentz transformation
Lorentz transformation has the same formulas as Special Relativity, but was developed independently. Can this serve as one evidence that Special Relativity is correct?
The answer is no.
Lorentz transformation was developed to explain the null result of Michelson–Morley experiment,
which was designed to detect the relative motion between the Earth and aether.
As no relative motion was detected, FitzGerald and Lorentz independently came up with the idea that bodies in motion relative to the aether are being contracted, which was later called FitzGerald–Lorentz contraction hypothesis, and with this came the Lorentz transformation.
Although Lorentz transformation has exactly the same formulas as Special Relativity, their physical meanings are different.
For Lorentz transformation, the aether serves as the stationary system, only a system moving relative to the aether needs the transformation.
So Lorentz transformation is one way formula, and will not cause any contradiction.
In Special Relativity, there is no such stationary system as the aether. Whenever we have two systems of relative motion, the formulas can be applied equally to any of them.
That's why so many paradoxes are created by Special Relativity.