Some approaches have a note, "Procedure NA at night except by prior
arrangement for runway lights". Let's say I make this prior arrangement
(presumably by talking to the airport manager and having him leave the
lights on for me), how do I deal with ATC?

When I ask for the approach, is the controller going to ask me if I have
made "prior arrangement" for the lights? Is my say-so good enough for him,
or does he need to get some official notice from the airport manager saying
it's OK to let him run the approach?