Please read the following article.
I attempted to write the following comment for that article, but their website wasn't accepting comments for some reason:
You can test the underlying web service that SPDesigner uses to lists these lists by appending "/_vti_bin/ListData.svc" to the site URL. You should find that on sites where SP Designer's list of lists works, this URL will return XML. On sites where SP Designer's list of lists doesn't work, you will get an extremely non-descript error.
In some instances you can still see the lists in "View All Site Content". If you click each individual list, you may find that manually enumerating through these lists may produce a useful error message. If you don't need that list, you can use the 'delete corrupted list using stsadm' command to delete the corrupt list if the list is not important:
stsadm –o forcedeletelist –url http://sharepointserver/lists/yourcorruptedlist
However, If you need to recover the data on that list, take a look at the correlation you receive from the attempt to view the list, and attempt to solve that problem - you may find a feature is disabled or something... Worst case scenario I expect you can recover the data from the database somewhere (maybe via SSRS?).*
For me, I found that the problems were caused by empty, unimportant lists. When I was able to successfully "manually enumerate" through that list of lists, then the underlying web service started working, and after closing and re-opening SP Designer, Designer started working too.
* Disclaimer: modifying SP or even viewing databases directly may leave your farm in an unsupported state. At this point I would recommend contacting Microsoft.