Did some online research and found the following information about Francis L Hughes (born circa 1835). In summary, by 1881 Hughes and his son had a retail store in Rochester NY selling toys and baby carriages (carriages were of their own manufacture). By 1884 they were selling Columbia and Victor Bicycles. Hughes continues to sell bicycles through the 1890's. The first reference I found for Lyndon Bicycles was January 1897. Not sure if he actually manufactured the Lyndon or bought it from a jobber and put his name badge on it. Ads still have him selling Lyndon Bicycles in 1900 but his building burns down in 1901 so I am assuming that was the end of his involvement with bicycles. I did not find any images of a Lyndon Bicycle. There are more period publications to look through. Without knowing Lyndon's model numbering system I would think yours being a No. 2 is earlier than latter so maybe it is a 1897 model. I also think wooden handle bars were most popular 1896-98. Did you find a serial number stamped on the frame?
From the book
Rochester Made Means Quality (published 2016
From 1884 History of Rochester NY:
Circa 1890 Ad:
Undated ads from the book
Rochester Made Means Quality (published 2016
November 11, 1895 issue of
The Referee listed names of bicycles being made at the time. Hughes was listed as making a Hughes bicycle:
December 24, 1896 issue of
The Referee says Hughes is selling Keating, Crescent, Cleveland for 1897:
January 1, 1897 issue of
The Referee lists Hughes making Lyndon Bicycles (earliest Lyndon reference I found
February 4, 1897 issue of
The Referee listing three models of Hughes bicycles:
March 19, 1897 issue of
The Wheel listing exhibitors at 1897 Rochester Bicycle Show:
April 22, 1897 issue of
The Referee reference to Hughes selling Crescent, Keating and Lyndon Bicycles:
1897 Hughes ad from the book
Rochester Made Means Quality (published 2016
February 11, 1898 issue of
The Wheel - Hughes is a director of a new company called Red Cross Rubber:
August 25, 1898 issue of
The Wheel describing Hughes' store:
October 26, 1899 issue of
The Wheel - Hughes testimony about Morrow Coaster Brake:
November 16, 1899 issue of
The Wheel - Hughes testimony in Morrow Coaster Brake ad:
Circa 1900 ad listing bicycles Hughes sold:
February 10, 1901 issue of
Hardware about Hughes' building destroyed by fire.