Lenses for night photography and auroras
In general, you'll want a fast wide angle lens for capturing auroras. And by fast, I mean f/2.8 or faster. The reason for this is to use the lowest ISO that we can (to reduce noise) and to be able to get to the shutter speeds needed to create star points rather than slightly elongated stars that don't know if they're in focus or not.
Some suggested lenses are:
Cameras with FX sensors:
Rokinon line of wide angle lenses. Specifically the 14mm f/2.8 and the 24mm f/1.4
Cameras with DX sensors:
Tokina 11-16mm f/2.8
Renting a lens
Some of the suggested lenses can be very expensive. But you can rent these lenses at a fraction of the cost. For example, the Nikon 14-24 f/2.8 is a $2000 lens. But you can rent it for around $200. The Tokina 11-16 is more reasonable at $525, but you can rent that one for around $100.