Posted: 30/03/2016 at 17:01
If the storm has broken some of the roots, it will be unlikely to ever re-establish itself solidly in the future even if you stake it, unfortunately. If you decide to do that, I would completely remove the old branch you mention. Any chance of uploading a photo of the tree in it's present condition? That would help us in suggesting a course of action.
Edit: just saw Dave's post - yes, they can take a heavy pruning which I would also advise but do be aware that lilacs can produce a lot of suckers after a hard prune.