From "The Library World" column of May 1916, reprinted in The Library Journal:
NEW YORK. La Salle. La Salle's New Public Library was opened to the public, April 6, in rooms in the postoffice building. One thousand well selected books are on the shelves — the larger share have been donated — and a reading table with the latest magazines is a feature. The Library Association has 102 charter members, and has been granted a charter by the State Board of Regents. It will be open three afternoons each week, Miss Marian V. Tompkins acting as librarian. 
The middle stretch of this library's history becomes a bit murky, so I contacted the library through Facebook and was able to confirm that the current LaSalle Branch Library in Niagara Falls is the La Salle public library discussed in The Library Journal.