Einstein agreed with the Lorentz theory

I have argued that Einstein never claimed this his special relativity theory was any different from Lorentz's, such as this:

The truth is that there was very little difference between the views of Lorentz and Einstein.

However I did not consider a Schwarz paper:

The only difference between Lorentz's approach and Einstein's is that Lorentz derived the transformation after an experiment forced him to, whereas Einstein starts with the generalized principle of relativity and derives the transformation from a necessary consequence of applying the second postulate.

That paper translates a 1907 Einstein paper as:

It required only the recognition that the auxiliary quantity introduced by H. A. Lorentz, and called by him "local time", can be defined as simply "time." ...

In what follows it is endeavored to present an integrated survey of the investigations which have arisen to date from combining the theory of H. A. Lorentz and the theory of relativity.

Taken literally, that reads as Lorentz having his own theory of local time, and Einstein claiming to have another theory called "the theory of relativity." But that is a mistranslation, as no one used the term "theory of relativity" in 1907. A better translation says:

Quote by Einstein 1907:
Im folgenden ist nun der Versuch gemacht, die Arbeiten zu einem Ganzen zusammenzufassen, welche bisher aus der Vereinigung von H.A. Lorentzscher Theorie und Relativitätsprinzip hervorgegangen sind.
In den ersten beiden Teilen der Arbeit sind die kinematischen Grundlagen sowie deren Anwendung auf die Grundgleichungen der Maxwell-Lorentzschen Theorie behandelt; dabei hielt ich mich and die Arbeiten von H.A. Lorentz (...1904) and A. Einstein (...1905).

Translated:
In what follows, the attempt is made to summarize into a whole the works hitherto emerged from the unification of H.A. Lorentz's theory and the principle of relativity.
In the first two parts of the work, the kinematic foundations as well as their application upon the fundamental equations of the Maxwell-Lorentz theory are dealt with; on that occasion, I relied on works of H.A. Lorentz (...1904) and A. Einstein (...1905).

That famous Einstein 1905 paper says the same thing:

we have the proof that, on the basis of our kinematical principles, the electrodynamic foundation of Lorentz's theory of the electrodynamics of moving bodies is in agreement with the principle of relativity.

That Lorentz theory refers to what we now call Maxwell's equations, the Lorentz force law, and the 1895 Lorentz paper giving a relativistic explanation of Michelson-Morley. Poincare criticized that theory in 1900 for not being fully compatible with the principle of relativity. Lorentz answered with a 1904 paper extending his theory to comply with the principle of relativity.

The technical content of Einstein's 1905 paper was essentially the same as Lorentz's 1904 paper -- responding to Poincare's conjecture that the theory comply with the principle of relativity. The main difference, as Schwarz explains, is that Lorentz show how the theory is a consequence of experiment, and Einstein takes a shortcut by using postulates instead. There were also minor terminological differences, such as saying "local time" or "time in the local reference frame".

No one else saw any difference between Lorentz's and Einstein's views, as the theory was often called the Lorentz-Einstein theory. Only decades later were they considered different, and now they have different Wikipedia articles: Lorentz aether theory and Special relativity.

Einstein spent much of his life bragging about his relativity originality, and in 1954 he gave this confusing explanation of how his theory was different:

By careful examination of the experimental facts, Lorentz found out that one has to think of the aether as rigid and acceleration-free (contrary to H. Hertz). Newton's space was "materialized" in this way. Though time didn't appear as a problem at first. Yet it became a problem, because it enters as an independent variable (besides the space coordinates) into Maxwell's equations of "empty space", upon which all electromagnetic processes were founded by Lorentz. Now, all would have been satisfying, when it would have been possible to demonstrate the state of motion of the aether ("absolute rest"). The systematic treatment of this problem by Lorentz led very closely to special relativity, because this problem forced Lorentz to transform spatial coordinates and time collectively. That he didn't make that step to special relativity, simply lied in the circumstance, that it was psychologically impossible for him to dispense with the reality of the aether as a material thing (carrier of the electromagnetic field). Those who witnessed this time will understand it.

Einstein believed in the aether after about 1916, but back in that 1907 paper, he had much more faith in electromagnetic fields:

Only the idea of a luminiferous ether as the carrier of electric and magnetic forces does not fit in in with the theory presented here; for electromagnetic fields do not appear here as states of some kind of matter, but rather as independently existing objects, on a par with matter, and sharing with the latter the characteristic of inertia. [Schwarz translation]

Einstein is taking a strange philosophical view here. When people back then talked about the aether, they often just meant the possibility of electromagnetic fields.

Lorentz does acknowledge that he had not abandoned the concept of a preferred frame. He wrote in 1910:

Provided that there would exist an aether: then one of all systems x, y, z, t, would be preferred ... Now, if the relativity principle had general validity in nature, however, one would consequently be unable to find out whether the reference system momentarily employed is that preferred one. Thus one arrives at the same results, ... To which of both ways of thinking one adheres to, we can leave to the judgment of each individual.

In other words, you can believe or not believe in an unobservable preferred frame. He wrote in 1914:

Einstein ... arrives at the abolishment of the aether. The latter is, by the way, to some extent a quarrel about words: it makes no great difference, whether one speaks of vacuum or aether. Anyway, according to Einstein it has no meaning to speak about a motion relative to the aether. He also denies the existence of absolute simultaneity.

Most cosmological models do have a preferred frame for time and stationary objects. That is why you can read stories about the age of the universe, and how some stars are older than other stars. So there is (probably) a preferred frame, and it does not have much to do with special relativity.

Those who say that special relativity somehow depends on there being no preferred frame are just wrong. There may or may not be a preferred frame, and it does not make any difference to the Lorentz transformations or any other part of special relativity.

Einstein does not mention Poincare, who introduced the spacetime geometry that is central to what everyone has called special relativity for the last century.