Hi Marianne,

Thank you for contacting the helpline. I believe this may be lilac leaf miner. The adult leaf miners lay eggs on the underside of a leaf, then the larvae hatch and feed on the green tissue between the upper and lower surfaces of these leaves. Once they have burrowed it is hard to see or remove them because they are protected within the structure of the leaf. Leaves will have brown blotches or tracks that can eventually merge together and cause leaf curling.

Leaf miners don't typically cause major damage, but can make the plant look pretty bad. To manage them, you can remove the affected leaves to stop the spread. Dispose of damaged leaves (composting them could continue the problem as they overwinter in soil) and keep the area free of weeds and leaf debris. 

Here's some more info:

lilac leaf miner

Lilac Info

Hope this helps!

You're Welcome! Please reach back out any time if you need to.