In a few months will be traveling from Calgary to Mumbai via Narita. I have a 21 hour, overnight connection at NRT. If I use the KAL lounge airside, which publishes itself to be open during the day only, can I remain there during the night?
The KAL Business Lounge closes at 8:50pm. While I've occasionally known an airport lounge to extend its hours due to flight delays, I've never seen one that allows people to remain once it does, in fact, close. So no, you will not be allowed to stay in the closed lounge overnight.
Sleeping in Airports has information about staying overnight at Narita, though for 21 hours, you have plenty of time to leave the airport, get a place to sleep, and see a little bit of the city.