Hi,
Have'nt got the answer to your question yet. It would be nice to find Arthur on an earlier Census to find where he was living in 1900 or 1910 - born Ohio, they could also have married there. I did notice that the 2 nd born son Ralph had the middle name of "LYON" and wondered if you had explored the possibility of that being the maiden name of Katherine.
Just a quick look at the passenger lists - bearing in mind Katherine was born about 1884 Ireland - threw up this one (birth date slightly out but that does not necessarily mean anything):-
New York Passenger ListKatherine Lyon - Born about 1881. Aged 18 years
Arrival Date: 21 Sep 1899
Travelling from Queenstown, Ireland to New York, on the SS Aurania.
Going to a sister Mary Lyon.
Maybe Shellyesq will point you in a better direction than I can but the link below is for the New Rochelle Public Library - it has the "Ask A Librarian " link. I wonder if this would be worth an e-mail to enquire if anyone could do a look up for marriage information for Arthur & Katherine or point you in a direction if that was'nt possible.
Have you found the death of Katherine ? Could be a possibility of further information if there was an Obituary Notice. Sorry I have'nt been more helpful for you but wish you the best of luck

Regards
Sandra
http://www.nrpl.org/