All right, apparently you have very strong and zealously fixed opinions about the truth on all of these matters. I’ll leave you to enjoy them in peace.
The Buddha taught that even arahants should continue to practice - SN 22.122 - which is why I am confused here. You suddenly want to talk about a special case of lived nibbana; I’m not sure where you’re trying to go with all this… we were talking about Secular Buddhism, and you seem insistent on some sort of distinction that isn’t really apparent, yet.
An Arahant can still learn - acquire new information but they don’t need to practice anything. The Buddha may have meant that the Arahants stay in the discipline i.e. continue to live as monastics?
Well, I think that leaves all the other parts of the conversation behind, so I’m off. It was a fascinating, if confusing, bit of rummage. With that said,
As you know there are the teachings about the ten fetters. Our practice must undergo change as we are released from fetters - and the remaining fetters are attenuated.
Those of us who are still practicing as putujanas - those whose lives are entangled in the 8 worldly concerns are not the same as Aryan practitioners.
For instance, a ‘stream enterer’ is freed from the fetter of ‘personality belief’. This means they have a deeper realisation of not-self than a beginner on the path. Their path has ‘changed’ from what it was before their progress of insight.
So, when we talk about ‘practice’ there are different levels of engagement as we move from the stage of a beginner towards full awakening (Arahantship).
As the path nears completion the practitioner becomes a living embodiment of the teachings. Finally, we don’t require the instruction manual. The heart tells itself what to do! You don’t need to practice something you have understood completely.
If the term ‘supramundane’ is troubling to a secular mind-set - giving rise to a bad case of dissonance - we could use something else. Perhaps, from subtle to gross or, from course to refined levels of understanding and insight. At some point in our practice we can dispense with ideology, theories, philosophy and practice. We can forget about practicing as Buddhists - if we wish. The Buddha was not a Buddhist he was an awakened being.
There is a difference between a practitioner who is still learning and an adept who has completed their training.
"Wisdom has the specific characteristic of penetrating the true nature of phenomena. It penetrates the particular and general features of things through direct cognition rather than discursive thought. Its function is “to abolish the darkness of delusion which conceals the individual essences of states” and its manifestation is “non-delusion.” - Henepola Gunaratana
Thanks for your understanding of secular Buddhism. I have finally understood why it is referred to as secular. It is Buddhism that is stripped of religious trappings. Hence, lay teachers, no religiously explicit shrines, no men and women in teaching positions in Buddhist robes. No devotional chants or homage recitations. Finally, I get it - better late than never!
It could be called: BCNC- Buddhism (Buddhism for clerks not clerics). 
I never used the term: a ‘lived Nibbana’.