Comment puis-je dire:
le lion mange durant la nuit
le lion mange à la nuit
ou est-ce que il y a autre manière?
It's possible to state a general fact like this
Le lion mange la nuit.
Of course it doesn't mean that the night gets eaten.
You can also use pendant or as you suggested durant, but the latter adds emphasis on the time span, which is probably not what was intended here. So the most natural phrasing with a preposition is the following:
Le lion mange pendant la nuit.