I'm assuming that you are talking about the refillable mugs at the resorts. I am not positive as I was there a long time ago, but I do think I remember them having a lid on them. I'm sure some DIS vets will follow up my memories with a definate answer.
Yes, they do have lids. There are 2 different kinds of mugs--the big fat ones have a lid with an open hole, but the skinny ones (the ones that fit in your car cupholder) actually have a little sliding cover that will close the hole in the lid. Since I too am a klutz with liquids, I usually get those kind so I don't ruin my clothes/car seats/bed sheets/carpet.....etc.
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