Can you use a Lorentz transformation with a venue in which there is no well-defined temporal limit, no well-defined temporal parameter? Would you be so foolish as to say such a temporal limitation does not exist when you come to realize the limit is not well defined such that it can be factored with a Lorentz transformation, but 'some' temporal factor is there based upon not yet well understood data?
Your way of dealing with ill-defined parameters is to assert they do not exist. Sadly, that approach is contradictory to what you claim you take as your position.