There is a neat site (Google)

PDF] THE LILAC TREE

whereon is a picture of a newspaper ad for the song by George H Gartland.

The title is "The Lilac Tree (Perspicacity)"

It was in a trade paper for sheet music companies by the looks of it and the publication date was in 1921. They have a small box in which the company selling the sheet music to the song said:

"We have had orders and programs giving more different titles than Heinz has pickles."

A page worth reading for those interested in song histories.