I think the best plan of action would be to cut it back now, but you will be sacrificing next spring's blossoms. Pruning now will give the plant the energy it needs to re-establish healthy roots. It's doubtful that the plant would recover well enough on its own to bloom anyway...it will have already set buds for next year and if it's browning, then they're probably already gone.
In the future, the best time to move or prune would be just after they bloom.
Good luck with it. The good news is that lilacs are pretty strong shrubs that can recover from this type of thing pretty well. As I said, I just wouldn't expect many blossoms next year.