Lethargy is not just general drowsiness (DD just wants to sleep when she's sick, that's not lethargy, that's recovery!). It's like nic explained. I would offer her the bb every time she wants it. Don't hold back or take her off. Breast milk is very gentle on her tummy and the best way to hydrate her. If she starts refusing the breast you can try the other suggestions, but I'd stick to just bm atm. You might be wearing it for the rest of the afternoon, but it will also be soothing her tummy and rehydrating her in the best possible way. Not to mention she's probably enjoying the comfort of being close and snuggling with you while she's sick.

Hope she's better soon, hun!