Lumo's UFN policy doesn't state that they issue the notice by email, rather that they issue a copy of such notice. A 'copy' is just that: a facsimile of another document rather than the original from which the copy is derived.
Admittedly, Lumo 'advise' that the email address they request is “one that you have access to at the time the notice is issued – you may need to show it to exit at a station” but fail to offer any explanation of why such immediate access to email is required.
If Lumo issue the original UFN to the passenger in the course of his journey then he is in possession of the document necessary for completion of that journey and exit through a barrier. In that case he doesn't need to receive an additional copy by email whilst his journey on a Lumo train is still in progress, and his ability to do so is irrelevant.
If, on the other hand, Lumo's practice is to issue the original UFN by email then (a) why refer to it as a 'copy' and (b) what is the hapless passenger without immediate access to email to do if the original will be inaccessible until after his journey on a Lumo train is at an end?
As written, Lumo's policy statement regarding the issue of UFNs appears to me either to be unworkable or to contain a completely irrelevant statement regarding immediate access to email.
What does seem clear is that a Lumo UFN, however it is issued, must state the full anytime single fare that is claimed for the journey. The OP says that at no point was this information provided in the course of travel on the Lumo train to Doncaster or subsequently at Kings Cross, either verbally or in writing. It remains to be clarified whether Lumo subsequently sent a copy of a UFN by post or email, as provided in its policy statement on UFNs. Subject to that potential complication, failure by Lumo to give the OP a notice containing the demand for a specific sum by way of payment of the fare claimed still seems to me to be a flaw fatal to any further attempt it makes to pursue the matter.
A failure to issue a UFN containing details of the fare claimed does not diminish the argument that the choice offered was between payment for a Lumo ticket or disembarkation at Doncaster, and that the OP chose the latter course. The non-issue of a UFN before the Doncaster stop lends some weight to that version of events, for, if Lumo were determined to seek payment of a fare for travel between Newcastle and Doncaster regardless of whether the OP chose to alight there, its official's appropriate course of action was to issue the requisite UFN before the OP left the train.
The Lumo official had no reason to suppose that she would once again encounter the OP at Kings Cross and thus have a second opportunity to pursue the matter. Since the alleged issue of a UFN is recorded as having taken place long after the Lumo train had arrived at Kings Cross, the inference must be that it was not until that second encounter that she decided to take advantage of the opportunity it presented to attempt the issue of a UFN, with the implication no such attempt was made in the course of the journey to Doncaster. I use the word 'attempt' as there seem to be grounds for doubting whether a UFN was ever actually issued.
