What's wrong with my lilacs?
This was a tough spring for many Minnesota trees and shrubs. We had warm weather in March, which may have stimulated your lilac out of winter dormancy. Then in April we had some very cold weather, which would have halted the development of buds that had previously broken dormancy.
Just because a branch lacks foliage does not necessarily mean it is dead. For these branches, use your fingernail to scrape away some of the bark to expose underlying tissue. If it is green, then that branch is not dead. If the tissue is not green and/or the branch seems very brittle, it is most likely dead. These could be removed at that time. If many of the bare branches appear to be living, then the lilac should eventually recover.
I would wait until blooming is done on what ever flowers may develop before doing anything else. Once blooming is finished, repeat the scraping process and again remove any dead branches. Be sure to water well during the summer. Immediately after blooming, add a small amount of fertilizer such as 10-10-10 around the base. Water this in well..
As I said,, if you discover that many of the bare branches are alive, then certainly do not remove the tree but give it ample time. Watch these bare branches for possible bud development. Some times when initial buds are lost, new buds later develop