Answer: Unfortunately, lilacs have the reputation for being difficult to propagate by tip cutting which is why they are usually propagated by digging a root sucker (at home) or by grafting (commercially). You may be able to root a tip cutting in the spring soon after it leafs out and begins to grow for the season. Since timing is a difficult thing to judge, you might want to take cuttings weekly over a month or so and hope you hit it right. Layering might also be an option if you have the luxury of time. Here are fairly detailed and illustrated instructions on how to do both of these methods. You may need to cut and paste the complete url into your browser to make it work correctly.
Also, although I do realize it would not be exactly the same as taking a start from your grandmother's plant, if you know which cultivar it is you might be able to purchase one. Best of luck with your project!
Q&A Library Searching Tips