Although most people have said that you can do a 1:1 substitution, I want to warn you that it's not always true.
The problem is that butter is part water, and so when you bake with it, it'll give off a little steam. If you use it melted it'll add water to the mix, which will develop a little bit of gluten when mixed with flour (first recipe, part of the second). You may need to adjust your recipe slightly. Typically, you want to reduce the amount of lard or other solid fat used by about 10-20%, and add back in 10-15% water (or other liquid; if you're dealing with un-melted butter, you may want to use vodka so it won't add to gluten development, but will still add steam).
That being said, one alternative might be to use clarified butter or ghee. Depending on how sensitive the person is, it might not be worth the risk, but for people with a milk protein intolerance who really crave the butter flavor they might be willing to try it. (and, as with the solid fat substitution, you need to adjust as it's all oil, no water)