In the spirit of the OP, what is a Lancastrian nationality or identity?
We could disappear down a rabbit hole here.
I would say that identity is in ones head and/or heart.
A country is merely arbitrary lines drawn on a map, with one set of laws governing one side of the line compared with a different set of laws on the other side. Look at the many conflict situations in the world where an ethnic group lives on both sides of a border and want independence from both. The argument for an integrated Europe is to remove those borders, and therefore the conflicts - we had a couple of major ones in the last century!
Great Britain, as with any island, does not fit that mould as it's borders are quite firmly established, them being a bit on the wet and salty side - nothwithstanding internal sub-divisions / nations.
People either side of a border will have more in common with each other than with those at the opposite end of the same country. Do the people of Yorkshire have closer ties with Lancashire or Cornwall? Do the Pennine Hill folk of Lancashire and Yorkshire have more in common with each other than with their sand grown 'uns in Blackpool and Hull respectively?
My view of the census generally is that it now asks far too many, often irrelevant questions. I know the topic is discussed by stakeholders at length, with debates between those who want to take advantage of the survey to ask as much as possible, against those who want to keep it short and simple in order to encourage its completion.
How many people live in a house, their age and occupation is relevant. Just what policy decisions will be influenced by peoples divulging of their religion, sexual orientation, thoughts on their nationality and ethnicity etc. I don't know. I saw no discernible benefit from declaring my household as being carless - there hasn't been a sudden rush to provide more buses to my area on the back of all the censuses that I have completed, nor has there been a determined effort to retain existing services, quite the opposite in fact.
I haven't yet had my invitation to complete, I will be filling it in honestly, as people should, but I will be also be leaving blanks and my own interpretation of certain questions. Do I feel persecuted by the government, not daring to leave my house in case I am stopped by the police and questioned about my movements? Yes, well I must be black Irish or something then.