My nethie - Henry has a very similar condition - the only difference with Henry is that he doesn't have a tear duct so Henry's treatment may differ slightly - but his symptoms will be similar to Lilac.
Having ducts flushed is, as far as I understand, a relatively simple procedure and doesn't usually involve any anaesthetic as such. It's a syringe with a long silicone thin tube which is then inserted through the eye socket and the tube follows the duct canal and then saline is flushed. The blockage should come out through the nose. And that's the positive result. It takes only a matter of minutes.
Is it likely to recurr? Percentage wise, probably. In Henry's case, because he doesn't have that duct, then infection is always a side effect because normally the tear duct would direct tears and fluid down to the nose and it would evaporate. But the eyes are warm and moist and an infection risk is always there I'm afraid. But - as long as your vigilant, then you can react quickly. Treatment if there is an infection, is usually simple and is a course of 3-4 penicillan injections which have to be done 24 hours apart at the same time every day for 3-4 days. It clears any infection quickly.
You just need to watch for any discharge - white goop on or around Lilacs eyes and surrounding fur. Try and wipe away as much as you can with a piece of cotton wool (damp) and dry it if Lilac will let you.
As long as you manage it and maintain a watch, then you will be best placed to act quickly. As far as I know, this will be a long term condition.
Hope this helps
Craig