Those two restaurants have been together for almost a hundred years and both very successful. The one next door to Lafayette is American Coney Island, not National.
Lafayette was founded by a Greek immigrant named Gust Keros in 1917.
In 1924, Gust brought his brother Bill to the U.S. and instead of going to work for Gust, Bill opened Lafayette next door........and the rest is history.
https://theculturetrip.com/north-america/usa/michigan/articles/the-story-behind-the-rivalry-between-detroits-two-oldest-coney-island-restaurants/