I don't see too many similarities between Nathaniel West's Homer Simpson in The Day of the Locust, and the famed father of Bart Simpson in The Simpsons animated TV series. Both of the characters are large and middle-aged, and the DOTL character is also a bit on the bumbling side, though nothing like the screw-up cartoon Homer. However, Matt Groening, the creator of The Simpsons, did acknowledge in 1990 that the West character was an inspiration for naming his Homer Simpson. In truth, Groening based his Homer on his own father, although he claims the only thing they have in common is a love for donuts.
There is no connection; it's all coincidence.