Browning lilac leaves are usually caused by either a lack of moisture or nutrients. We've had a fairly wet summer so far, so it seems unlikely that drought is the problem...unless somehow the roots have grown large enough in a circular fashion to choke themselves from being able to adequately supply the needs of the lilac.

It would be a good idea to conduct a soil test to ascertain if the soil is supplying the needed nutrients for good health. Self-mailer soil test kits from the Michigan State University Plant and Pest Diagnostic Lab can be purchased in person at MSU Extension offices or online from the MSU Extension bookstore (shop.msu.edu). The cost is $26.

Full instructions are there on that site and also come with the kits. The Lab will make recommendations for any needed soil amendments. Be sure to tell them what is planted in the area being tested. Further information can be found in the link below:

https://www.canr.msu.edu/news/soil-testing-returns-through-msu-extension

Well-drained soils are imperative for lilacs; they cannot tolerate wet conditions, even for short periods. They prefer soil pH to be on the alkaline side, but tolerate neutral to slightly acidic soils as well. Mature plants need little supplemental water except during extended periods of dry weather. Avoid wet or soggy conditions.
Lilacs generally do need need fertilization, so see what your soil test says about the nutrient and pH levels of the soil around your lilac. If needed, apply a granular (not liquid) fertilizer formulated for woody plants in late winter/early spring. Lilacs bloom on old wood, so should only be pruned immediately after blooming. At that point, it can be trimmed, shaped, or thinned. Any suckers are best removed in mid-late summer, as that minimizes their
recurrence.

A 2-3" layer of mulch around the trunk of your lilac would help the soil retain moisture. Be sure to keep the mulch at least 2-3" away from the bark. 

Of course, there's also the possibility of pests and diseases damaging your lilac. Lilacs are pretty resilient, but sometimes pests like aphids or diseases like powdery mildew can cause the leaves to brown as a sign of distress. Examine your lilac leaves carefully, both the upper and lower sides, to see if there are any insects hiding out there and possibly sucking the nutrients out of the leaves. Powdery mildew is a fungal disease that causes white, patchy blotches on the upper surface of the leaves. The browning would come later.

Lilacs are like old souls. And we know your lilac tree is quite old because it was your mother's before you. Lilacs have their quirks, and sometimes the older leaves will turn brown and make way for fresh, young leaves to take the stage. It’s their way of freshening up and making room for new growth.

Lilacs want a rich soil, give them
manure. They do better in full sun but do OK in shadier light.

If none of these things seem to be the issue, you may wish to consult a certified arborist. An arborist is a certified and generally insured expert in trees and their problems. He or she can examine your tree and make recommendations regarding the health of the tree and any needed judicial treatment or pruning. Hiring a certified arborist will ensure that you are getting a knowledgeable and qualified tree specialist. You can find a certified arborist in your area here: 

http://www.treesaregood.org/

Click on "Find an Arborist" at the top of the page; then click on United States from the pull-down menu. Then enter your State and City. This should bring up a list of certified arborists nearest to you. Or you may be able to locate one under "Tree Services" in your local Yellow Pages.

Your email MADE my day.  I will be stopping into the extension this week to pick up the soil testing kit

My pleasure. Good luck!  I too have plants that I cherish because I inherited them from my mother and my grandmother.