Q.Can I propagate lilacs from a large broken branch
Following a heavy wind, 1/3 of my very old lilac bush is on the ground. It has been there for 3 weeks & is now blooming. I would like to save these branches. Is this possible to do without the root?
First, you're going to want to prune back the broken branches. Read this article on pruning lilac for som tips: https://www.gardeningknowhow.com/ornamental/shrubs/lilac/pruning-lilac-bushes-when-to-trim-lilac-bushes.htm
LIlacs are very difficult to propagate from cuttings, as this article explains: http://aces.nmsu.edu/ces/yard/2005/051405.html
I don't know if it's too late in the year for cuttings from your lilac to root, but no reason not to try. Just be aware that new life for your lilac is probably going to be in the form of new growth from the roots and the pruned branches.