There are 2 ways to do this. One is as a redemption, and it doesn't greatly matter when you book. The surcharge component with the cash about can come down during a sale but not reliably so, and not from NCL typically. The other way is to book a cash ticket and then use Avios as part payment. This is typically isn't good value, I tend to disparage it as only suitable for those who flunked maths at school, but if you have lots of Avios and nothing else to spend them on then actually there is an argument. Clearly cash tickets do get cheaper in sales, though when this happens the Avios conversion tends to go even more adverse.

In that respect consider split tickets, once you understand the risks. The reason being that LON-NYC is hugely competitive, whereas NCL-NYC is not at all competitive, several major players aren't in the game. Also consider Aer Lingus from DUB (and SNN) since their Avios pricing can be a lot more reasonable, again it may be best to split tickets, or pay cash or use Ryanair. SNN is served by Ryanair from EDI.