How to use Dropbox for applications with Lion Versions support?
My take on this is that Apple does not want users to see iCloud as another Dropbox or (even worse) another iDisk. Although I am not certain of what I about to write, my theory on iCloud based on what I have read so far is that there will not be an iDisk-like drive or a Dropbox-like special folder. Instead, iCloud's approach will be app-centric in that you will open the app you want and then get your files from iCloud regardless of which iPad, iPhone or Mac you're using at the time. In the practical sense, that most likely means that iCloud will "magically" get you the latest file as you switch contexts, but not the file's Versions history--that will be for now a Lion-only feature. 

I do not anticipate Dropbox integrating with Versions or iCloud any time soon because it is not in the best interest of Dropbox for you to use iCloud and vice-versa. Especially considering how both have a vested interested in earning your storage needs business (And this is even more true for Dropbox than it is for Apple). At the technical level, there is no reason why they wouldn't be able to coexist: Lion would see the Dropbox folder as any other folder and allow you to keep its Versions history. Dropbox, in turn, will see the hidden folders used by Versions as folders it needs to sync up--unless Dropbox does not currently support syncing hidden folders. I have not tested to see what Dropbox does with them 

It is important to remember that Dropbox's very own version history is kept at their server. That means that there would not be a physical conflict between the historic files Dropbox keeps track of and what Lion keeps track on that same folder for Versions. It will be up to you to choose where to go and look: On Lion's friendly Versions UI or on Dropbox's web-based file history. Of course, the caveat is that the individual historic entries won't be exactly the same. I guess you can say there will be two "versions" of the same story (pun intended). 

I do not think there is a need for a workaround as there really is no technical conflict. iCloud and Dropbox will both do their thing and I will probably end up using Versions in Lion to browse the file history of all of my files, even those in the Dropbox folder, because it is friendlier to use. If I cannot use Versions on a particular file because its app doesn't yet support it, and if this is a file that I have in Dropbox, then I will go and take a look at the Dropbox website to get its version history. Hope this helps.