The concept of Lorentz invariance (i.e. the "constant speed of light", or more generally Lorentz symmetry (LS) or Lorentz covariance) is local principle (a theorem) in general relativity and the main global principle (a postulate) of special relativity. It means, on the validity of LS depends the predictability of many quantum field theories, which are using LS as the one of their postulates, including (but not limited to..) string theory. The quantum gravity, the LQG theory in particular, is less dependent to LS being general relativity based, so it allows Lorentz symmetry violation (LSV) in certain extent.
Nevertheless the concept of LS still remains heavily misunderstood by contemporary physics. The strong respect to relativity leads physicists to widespread belief, the LSV is a sort of boundary phenomena, which is especially difficult to detect. Whereas by AWT it involves whole range of quantum uncertainty phenomena, instead. In certain sense even Brownian noise, which can be observed by naked eye under certain circumstances can serve as a tangible evidence of LSV. In the quantum mechanics, the LS is always violated by its very nature, which leads to the violation of causality, the fragmentation of time arrows into many time dimensions (a multi-verse or many worlds concepts) and so-called the landscapes of many possible solutions (fuzziness) of superstring and quantum gravity theories.
From AWT follows, the LS should be violated on both ends of mass-energy density/space-time scales, because the Aether forms a nested foam with mutually penetrating and vanishing levels of density gradients. As the most pronounced manifestation of LSV at the cosmic scale can serve the presence of dark matter foam (the polarization of CMB in particular), the gravitational lensing and the gamma ray dispersion, which manifests itself for example by GZK limit and by retardation of gamma ray portion of flashes of distant supernovas. No wonder, some string theorists aren't very happy from these observations, because they're realizing, no formally consistent theory could predict the violation of its own postulates...
As above stated, here are some theories, which are predicting the LSV at the gamma ray end of EM spectrum, like LQG or Kostelecky theory. The problem is, these theories are rather formal and complex, therefore their proponents cannot understand well, what they're really looking for. From this perspective, the wider acceptation of Aether concept could save a lotta effort and frustrations for scientists and money for publicity. The straightforward example of LSV is the GZK limit (gamma ray suppression at the cosmological scales), which can serve as a close analogy of so called the Rayleigh dispersion of blue light by density fluctuations Earth atmosphere. By such a way, the thick layer of vacuum protects terrestrial life from energetic gamma rays by the same way, like the Earth atmosphere from UV rays. By AWT these density fluctuations are formed by fluctuations of cosmic microwave background (CMB), i.e. the very same noise, which everyone can detect by common TV-receiver. By AWT the photons of CMB are behaving like sparse voluminous density fluctuations of vacuum ("blobs"), which are dispersing the photons of gamma rays and cosmic radiation above the 10E+19 GeV scale.
The LSV by mutual interactions of gamma ray photons and photons of CMB can be understood easily, if we realize, by special relativity the photons are massless bosons of long-distance interaction, so they cannot interact mutually. Therefore every photon-photon interaction (including the well known pair production) should be considered as a direct violation of LS. By AWT this violation is nothing strange, indeed - because it predicts the non-zero rest mass of photon as well. We should realize, Lense-Thirring effect is contradicting the zero result of M-M experiment directly. Therefore we should observe some minute frame dragging effects even at the case of M-M experiment, especially at the large space/time and/or mass/energy density scales.
"In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the speed of propagation of light varies with position ("die Ausbreitungsgeschwindigkeit des Lichtes mit dem Orte variiert"). Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the case. We can only conclude that the special theory of relativity cannot claim an unlimited domain of validity; its results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light). Since it has often been contended by opponents of the theory of relativity that the special theory of relativity is overthrown by the general theory of relativity..."
(Ueber die spezielle und die allgemeine Relativitaetstheorie, Einstein 1916, chap. 22)