Fortunately, its history is well-documented. Gerry Vogel's great Avon Lake Images of America book for Arcadia Publishing includes a vintage photo (below) of the house courtesy of Gerry Paine, and a capsule history.
There's actually a lot of information online about Anson Titus and his family, due to his prominence. The avonhistory.org website reveals that Anson Titus taught school in a log school house on Moore Road, and that he fought in the War of 1812.
Two more photos of the home can be found on the Cleveland Memory Project website. The first photo (below), also courtesy of Gerry Paine, is believed to have been taken around 1910.
The second photo (below) was donated to the website by Nancy Jane Nelson Abram. (Ms Abram wrote a self-published two-volume history of Avon Lake, which is available at the Avon Lake Library.)link to the www.findagrave.com page for Anson Titus.