So in Morrowind (and maybe in Skyrim? I'm not sure) there were Dwemeri ghosts running about in ruins which makes me believe that dead Dwemer weren't subject to Kagrenac's folly. Well, would this extend to any old mages that decided to become liches or any other Dwemer that cheated death? Would it be possible for us to delve into a Dwarven ruin and encounter a long lost lich at the bottom? I just had the idea randomly and thought it would be cool if we could converse with an old Dwarven lich.

Theoretically, sure. I don't think the Dwemer's philosophy/culture was the sort that would lead one towards lichhood, though.

1. Liches are generally not quite talkative.
2. The dwemeri ghosts are a mystery, since all the dwemer disappeared when they (and their souls) were unmade on Mundus. The one and only known exception avoided this by being in the Outer Realms at the time. Long story short, where do the ghosts come from? The only reasonable explanation is that they became ghosts before Kagrenacs folly. That's a very long time, even for a lich.
3. The dwemer were more technology/magitech inclined, thus it's quite unlikely that anyone choose to become a lich. Apparently they had other means of longevity/immortality.