Miasmom: That is not a dumb question at all—because of their place as an animal product but not meat, they get confused as dairy quite often. And it makes sense—most non-meat animal product foods are dairy. They just aren’t.
A few options: you can get lactose free milk (lactaid) and cook as usual. You can use soy milk. For butter, if you go to the local health food store or whole foods, there will be butter-eqsue things that are meant to replace dairy in baking. For baked goods you can replace butter with oil, like La_Chica said or with apple sauce (though the conversion is a bit different).
If you want to find some lactose free desserts, look up vegan recipes. While you can use eggs, you don’t have to so any vegan recipe is already made to your specifications.
I like making biscotti. The recipe I use is here: http://paperbagged.livejournal.com/7247.html#cutid1
I generally use her basic recipe and add the zest of one orange and a big handful of craisins. Yummy!
If you want something more desserty, I’d go with a crisp/crumble. Basically a cobbler but with an oatmeal topping. Use a butter replacement in the topping and you are good to go!