SR, LT and so on relies on the Einstein convention of simultaneity
The Lorentz transformation does, because the Lorentz transformation is defined as transforming between standard inertial frames. But "SR" does not, because, as I have said, you can do calculations in flat spacetime in any coordinates you like; there is no requirement that you have to do them in a standard inertial frame. Of course the transformations between coordinates that aren't standard inertial frames won't be Lorentz transformations, but so what? The physics is still the same.