You have just opened a second string with essentially the same question: bad board manners!
If you can find the late John F. Kirkland's book "The Diesel Builders: vol. 1: Fairbanks Morse and Lima-Hamilton," it will help with the diesel side: an appendix has a complete list of Lima diesel locomotives.
I don't know of an available list of Lima steam locomotives. "Railroad History," the periodical published by the Railroad and Locomotive Historical Society, regularly publishes rosters of individual railroads.
I would hope that Lima's records were deposited somewhere: maybe with the Smithsonian? It seems, therefore, probably that the truth is out there... somewhere! Good luck with your research. Other people are probably also interested, so if you find something helpful (like: which library has Lima's records and what the catalogue number is), please report back to us!