Michelson was convinced that the null result meant that the Earth carried a layer of ether stuck to its surface. If so, the experiment would have been performed at rest in the local ether, which would explain the null result. ...No, FitzGerald and Lorentz never said that all the frames should agree about the value of the contracted length. Lorentz had his relativity theorem that observers in different frames could use the same equations.
Lorentz thought that Michelson-Morley’s null result could be understood in a very different way. He considered that a body moving in the ether suffered a length contraction due to its interaction with the ether. The interaction would contract the body along the direction of its absolute motion V, but the transversal dimensions would not undergo any change. ... This Lorentz’s proposal of 1892 had been independently advanced by FitzGerald three years before. This proposal did not mean the abandonment of the belief in the invariance of lengths. The contraction was a dynamical effect; it depended on an objective phenomena: the interaction between two material substances. The contraction should be observed in any frame, and all the frames should agree about the value of the contracted length. ...
Noticeably, the relativistic length contraction [of Einstein 1905] has the same form proposed by FitzGerald and Lorentz to explain the null result of Michelson-Morley experiment. However, its meaning is completely different. Lorentz considered that13 the contraction was a dynamical effect produced by the interaction between a body and the ether. For Lorentz, V in Eq. (26) was the velocity of the body with respect to the ether, and the contraction was measured in all the frames. In Relativity, instead, the length contraction is a kinematical effect.
There is no simple answer as to whether the contraction is caused by the motion, by the aether, by electromagnetism, or by what. The preferred explanation is that it is an illusion from the geometry of spacetime.
Sometimes people say that it is wrong to describe the contraction as being caused by motion thru the aether. To be wrong, you have to add hypotheses that make wrong observations possible. If you also assume that the aether defines one frame, that the contraction is based on the velocity thru the aether, and that a separately moving observer would see the same contraction, then you get a disagreement with experiment. But what FitzGerald and Lorentz said was consisent with experiment.
The above paper has some historical explanation of special relativity, but its attempts to credit Einstein are inaccurate.