If it’s not a physical issue (not even a nutritional one), it’s possible that it’s a psychological one, anonymous. If that’s the case, then it could be any number of things. Has she experienced trauma recently? Does she have a partner? Is this bout of lethargy a one-off happening, or has your banette experienced anything similar in the past?
Either way, I would highly suggest beginning with communication. Banette, like many ghost-types, are actually highly intelligent and in possession of a level of sentience that nears human thought. In other words, make it abundantly clear that you will always be there to give her whatever she needs to feel safe and happy, whether it’s affection, someone to listen to her ghostly moans, or some sort of distraction or extra outlets for venting.
Moreover, be sure she gets plenty of rest, hydration, and food, and be sure the food she gets meets her nutritional needs. Even basic care can improve a pokémon’s mood considerably, and you’d be surprised how much a lack of water or food can damage one’s spirits.
In all, while I unfortunately can’t guarantee that this will do the trick, it sounds like you may need to assist your banette in administering self-care. Treat her gently and with patience and teach her to do the same, and you may see a bit of her old self growing back.
The Pokédex According to Bill 