There is no such thing as 'Lorentz ether theory'. It's a myth. A pseudoscientific myth.
'LET' cannot be a scientific theory. It has exactly the same formulas, exactly the same mathematical model as Special Relativity does. So effectively it is equal to the Special Relativity theory.
That's funny. If it is exactly the same theory, but is not a scientific theory, that means that SR is not a scientific theory too.
Any numerical prediction 'LET' could give would also be given by SR. (Converse is not true: SR gives some general predictions that 'LET' fails to give, but does not conflict with, and those predictions hold.) By the criteria of scientific theories, it cannot pass as a separate theory.
Clearly wrong. In this case, it is a separate theory, with different predictive power.
So no experimentum crucis is possible to distinguish between them.
Wrong. In this case, an experiment which falsifies the more general predictions made by SR would falsify SR but not LET.
And what is more, Lorentz has nothing to do with this 'theory'.
Quite irrelevant. The meaning of LET is close to the views of Lorentz, the theory or interpretation is important and interesting enough to deserve a name, and LET is the name which is widely used.
Also, a name 'Lorentz theory', when met in a trusted context, does not refer to the Special Relativity theory or some ether theory. It refers to the 'Lorentz electron theory', meaning the theory of electricity in substances, conductivity, polarisation, optical properties and so on.
So what? We are talking here about LET, not LT.
But let's have a look at the difference between LET and SR:
It is a statement that everything in the world, every law of physics, either known or unknown, obeys the Principle of Relativity, and thus the Lorentz invariance. So, any new fundamental law of physics we would ever discover, would have the Lorentz-invariant wording (in its most general form). 'LET' fails to predict this, because it views the Lorentz invariance as a particular fact of only those laws we know at the moment, and there is no cause for new laws to have the same property.
Quite artificial.
When SR was first formulated, it covered only two theories: classical point mechanics, and the theory of classical elecromagnetic field. In the next years many more fundamental theories emerged, in rough outline: the theory of gravitational field (GR), quantum mechanics, the theories of quantum electromagnetic field, of strong interaction, of weak interaction. All of these theories were found to be Lorentz-invariant, that is, the phenomena themselves, new and unknown to the physicists of 1905, are all obeying the Principle of Relativity. This is a very non-trivial fact, and it should be entirely accounted in favour of SR.
First, GR has a different symmetry than SR. You cannot even define a Lorentz transformation to a global GR solution with nontrivial topology.
Then, gravity was known 1905, and the first attempt to develop a theory of gravity in agreement with Lorentz symmetry was made by Poincare 1905. It was not successful, but that's not the point - it was a natural part of the approach of Lorentz and Poincare too, no need for the Einstein-Minkowski interpretation.
So, "entirely accounting" the success of the simple idea to try to make other theories compatible with Lorentz symmetry too is unjustified.
What is more, the very concept of ether fails the same way, and even calls for search of Lorentz-breaking laws. Of course, the search is interesting and important for physics by itself, and it is conducted permanently, but without any relation to ether. The search always fails, for about a century. And even if it would find something not invariant, it would be called something else, not ether, maybe some unknown vector field of non-zero value, because the conceptual framework of physics has changed fundamentally, and new concepts are incompatible with the very idea of ether.
Of course, many people have recommended me to use another name for my theory instead of "ether". But not because there is something incompatible between the modern ether, which gives the particles of the standard model of particle physics as well as the Einstein equations of GR in a natural limit. The only reason is a political one: "Ether" is an unpopular word in mainstream physics.
But there is nothing incompatible with the very idea of ether in modern physics. Only in modern metaphysics.
So, SR is strongly supported by all that evidence, and 'LET' is not.
Wrong. First, not a single thing is mentioned where a prediction of LET is not fulfilled.
Then, if we would really apply the concept proposed here, then it is easy to find an experimental falsification of SR which does not falsify LET. You don't believe?
Take a look at the proof of Bell's inequality. Without knowing anything about quantum theory, but seeing Bell's theorem and its proof, everybody would have accepted Bell's inequalities as a prediction of SR. Instead, in LET it cannot be excluded that there are some yet unknown possibilities for superluminal causal information transfer, so it would not be a provable theorem in LET.
But we know today that Bell's inequalities are violated.