After using it for a few days and having an account for a few hours (this is my first comment), I don't think it will ever directly compete. But I think it does have chance to represent a "significant minority" of internet traffic if it doesn't peter out early on, and it may already be passed the threshold for that happening.
You'd never say email can "compete" with twitter, but it's still a significant way people interact with the internet. If lemmy does for independent communities and niche forums what email does for messaging, I'd consider it a huge success!