I lost a lilac bush to the sidewalk plow this winter. Most of the plant was lying on the tree lawn, in two large pieces.
We’ve only had two days of warm weather, so my guess is that it’s mostly still alive. I cut off all the intact smaller branches, which had green, healthy-looking cambium, and brought them inside. They are now sitting in four vases, with water.
It was a very pretty lilac, and I’d like to root some of the twigs if I can. I’m pretty sure my next door neighbor started two lilac bushes when I was a kid by rooting some flowering branches.
I’ve only had luck digging root shoots with lilacs. I wanted to try air layering, but had enough digging bits, so didn’t try. You might try a very damp soil and hormones with a humidity dome or milk jug. Somehow the commercial places get starts, just don’t know how.
If there’s pieces of root in ground still, it may sprout out. Layering is a wway to propagate.
If I was going to try cuttings, I’d try in June or July.
(Unfortunately you don’t have that option…so try it in water, but I don’t think your odds are real high.)