All that can presently (July 2023) be gleaned about The Lynotte Sisters from sheet music covers and by Internet searching is that they were presumably American actress/singers who have been featured on just one work namely Trading Smiles (1907) words and music by Don Ramsay, published by Walter Jacobs, Boston, Massachusetts, USA
Their portrait on the left is taken from that same work.
Surfers are welcome to contribute any further information about these performers.