Alas the NCL lounge is closed and no third party arrangements have been made as far as I know. On the outbound you would have access to the Ba lounge at Heathrow.
On the return you will need to clear security at Heathrow because of the terminal change (even though you landed as domestic and would not if staying in the same terminal). I don’t believe any *Alliance lounge is open at Heathrow.
I don’t think there is anything unusual about ticketing a rival’s flight but UA probably don’t expose it easily because they want to route you on the Star Alliance (for NCL with LH via Germany).
I’m not sure how BA would assess the baggage allowance. They would normally apply the greatest allowance on the journey but I don’t know if they can see the UA rules.
Priority luggage is easy - BA don’t do it. Yes they may put a label on it but if you see the Oneworld page BA are explicitly excluded from priority luggage. I’d imagine UA will bit see it as priority.