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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.