Your Dwarf Korean Lilac tree is actually a DKL shrub grafted to a standard trunk. They do typically have smaller leaves than a common or french lilac. They need 6-8 hours of sun each day.

Yours does not look very healthy. Check to make sure that it was planted at the correct depth - right at the root flare. Also be sure to move any much away from the trunk. The mulch should’ve be there to prevent moisture loss. 

With a new tree be sure it gets enough water for the first 3 years. If we don’t have rain, give it about 10 gallons a week and water until the ground freezes. This will help it get through the winter. 

You could do a soil test to see if it needs nutrients. You can find instructions here: https://soiltest.cfans.umn.edu/testing-services/lawn-garden

If you purchased it from a nursery you should have two year warranty on it. We had some good cold snaps last winter so that may be stressing it out. Be sure to water this summer if we have another year of drought.

https://extension.umn.edu/trees-and-shrubs/lilacs