If the Bulls were more ready to make noise in the playoffs right now, Rose might not be a bad option since at that point we'd be looking at short term improvement. That's not the case we're in. Technically, from a fit perspective Lonzo has what the Bulls want on paper, not that Rose doesn't skill wise, but the age thing is going to be a factor.
Though if the Bulls are looking for stop gaps, then technically Rose would fit (though career wise he may still look elsewhere), or you look at a guy like Jeremy Lin who does a lot of the same things and has nothing to lose