I assume you've looked at chinchillas2home.co.uk/safewoods.htm, where of course lilac isn't listed. I tried looking to see if anything even RELATED to lilac was listed (they are related to olive trees) and of course had no luck there. There is a guide towards the bottom of the page on how to judge based on sap leakage (if it's practically oozing out from under the bark near a cut, that's a bad sign) whether or not a certain wood is safe. Safest bet, is to not give it to your chin unless you're sure.
And if you decide to use it, all of the above!