... through the brilliant confirmations which the electrodynamic theory of H.A. Lorentz has experienced. That theory is founded, namely, on the assumption of a stationary immobile aether: ...The quote is misleading. Here is what Lorentz said in his 1895 paper:
It is not my intention to ... express assumptions about the nature of the aether. ... That we cannot speak about an absolute rest of the aether, is self-evident; this expression would not even make sense. When I say for the sake of brevity, that the aether would be at rest, then this only means that one part of this medium does not move against the other one and ...Einstein said the same thing in his 1909 paper:
This contradiction was chiefly eliminated by the pioneering work of H. A. Lorentz in 1895. Lorentz showed that if the ether were taken to be at rest and did not participate at all in the motions of matter, no other hypotheses were necessary to arrive at a theory that did justice to almost all of the phenomena.Thus they both say that Lorentz needed no hypotheses about the aether except that it did not participate at all in the motions of matter. Some people read a lot into that "at rest" phrase, but Lorentz explicitly disavows meaning an absolute rest of the aether. He only means that he is rejecting Stokes' view.
Einstein's 1907 paper takes a little more explanation. That Einstein quote on Lorentz's assumption is from a paragraph on Galilean invariance. "That theory" refers to Maxwell's equations, which Einstein goes on to say "are not so constructed that they go over into equations of the same form upon application of the above transformation equations."
Einstein only starts discussing the Lorentz 1895 theory in the next paragraph. The paragraph after that says that the Lorentz-FitzGerald contraction was "ad hoc", and then "It appeared thus that Lorentz's theory had to be abandoned again, and replaced by a theory whose foundations agreed with the principle of relativity". He then credits that replacement theory to Lorentz 1904 and Einstein 1905.
I read this as saying that there are 3 Lorentz theories. Lorentz-1 is Maxwell's equations, aka Maxwell-Lorentz theory, with Galilean transformations for a different velocity frame. Lorentz-2 is the Lorentz 1895 relativity paper. Lorentz-3 is the Lorentz-1904 paper and Einstein 1905 paper. When Einstein says "Lorentz's theory had to be abandoned again", he means that Lorentz was abandoned once going from Maxwell-Lorentz to Lorentz-1895, and abandoned a second time going from Lorentz-1895 to Lorentz-1904.
Thus I do not agree that the "fundamental assumption of Lorentz's theory" of 1895 was the stationary aether. I do not think that Lorentz or Einstein would have made such a statement.
Lorentz said in that 1895 introduction, "so far none of the two contested theories, neither that of Fresnel, nor that of Stokes, were fully confirmed with respect to all observations ... By that I was long ago led to believe that with Fresnel's view, i.e. with the assumption of a stationary aether, we are on the right way." Lorentz was scrupulous about crediting others. He was careful to distinguish Fresnel from Stokes, and to say he preferred Fresnel. He goes on to explain the "difficulties for Fresnel's theory". So he likes Fresnel better than Stokes, but Fresnel is not the foundation for his proposed theory. The foundation is Maxwell's equations, Fizeau, and Michelson-Morley.
By comparison, Einstein's 1905 paper said only this about the aether:
The introduction of a “luminiferous ether” will prove to be superfluous inasmuch as the view here to be developed will not require an “absolutely stationary space” provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place.Einstein was saying essentially the same as what Lorentz said -- that he was avoiding assumptions about the aether, that there is no absolute rest, and that motion is relative.
As Lorentz's theory was well-known in 1905, the burden was on Einstein to explain how his theory was any different from Lorentz's, if indeed he was claiming a difference. Einstein's 1907 paper describes his 1905 paper as being essentially the same as Lorentz's 1904 paper. Einstein only claims minor differences with Lorentz. The main one was where Einstein claims a terminological advantage over Lorentz's 1895 paper:
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."This point about time was not original to Einstein. Poincare wrote in a 1900 paper that Lorentz's local time is the same as the time measured by clocks. (And Einstein acknowledged in 1906 having read Poincare's 1900 paper.)
Most of these points are also discussed in my book. Einstein's 1905 relativity paper is widely considered to be one the greatest scientific papers ever written, but it is hard to find anything original about it. The original work was done by Lorentz and Poincare, and Einstein added nothing substantial.