I understand that some dogs totally ignore pigs, and seem to get along just fine.. but even if they aren't a 'hunting type dogs' doesn't mean that something couldn't happen..
In my opinion there is no reason to take that risk, putting a lid on the cage, and/or putting the cage in a room where the dog isn't allowed worth the extra effort just in case something did end up happening..
I have 9 dogs, 3 of which are considered 'hunting type dogs' as they are all or part Dachshund.. 4 of the 9 dogs are under 10lbs, 3 are under 20lbs and the other 2 are about 40lbs. They are all incredibly sweet and have never hurt another animal, or shown the slightest insinct to hurt another animal (including squirrels and such) but I still have my hamster, and cage for guinea pigs (for when I get them) in a room that none of the dogs are allowed in. If I wasn't able to do that, I would at least put the cage up high and add a lid.. its best for the safty of the animal.