Personally, I subscribe to the idea in Danny Peary's great, three-volume "Cult Movies" books from the 80s. In the first volume, he writes about "El Topo" and "Pink Flamingos" and "The Texas Chainsaw Massacre", but he also writes about "Casablanca" and "It's a Wonderful Life" and "The Wizard of Oz".
Cult movies tend to be offbeat and controversial, but the most important thing about them is that they inspire an unusual amount of devotion compared to other movies. That's Rule #1.
"Eraserhead" played for YEARS at some theaters for midnight shows, in large part due to repeat business. In the 1970s and early 80s, before home video was everywhere, "Casablanca" occupied a similar place for repertory theater owners. It was one of those films that reliably brought in an audience, many of whom had seen it before. (In his essay from 1980, Peary writes about going to see "Casablanca" in theaters in the 70s and seeing some people show up dressed like Bogart, in the trenchcoat and hat, decades before anyone ever thought of the term "cosplay").
So, yeah, I can see "The Big Lebowski" maintaining cult film status. A whole bunch of movies came out in 1998. Not many of them of have international meet-ups devoted to them.
I never went to one of these Big Lebowski-Fests. I don't know anyone who ever went one. But apparently a bunch of people did.
Sounds like a cult to me.