All that can presently (December 2022) be gleaned about
Lillian Ashley from sheet music covers and by Internet searching is that she was presumably an American actress/singer who has been featured on 2 works published between 1905 and 1912.
Her portrait on the left is taken from
My Irish Molly O (1905) music by
Jean Schwartz, words by Wm. Jerome and published by
Jerome H. Remick & Co., New York & Detroit, USA.
Surfers are welcome to contribute any further information about this performer.