Do you have any male Lilly relatives that had their Y-Chromosome DNA tested?
If not, could you encouage them to have the test run?
If so, can you share the results and the oldest known Lilly ancestor?
The American Lilly Family lineage is uncertain because Gustave Anjou published a Lilly genealogy book in 1898. He connected three major American Lilly families to the French Lilli family in the 1600's.
However, Gustave Anjou turned out to be a fraud who embellished his work with false lineages.
Y-DNA testing would help determine the ancestors of our oldest known ancestor, Samuel Lilly (b. abt 1699 England, d. 1758 PA). We don't know whether he was related to the French Lilli family or not.