The hope here is for it to become a standard license in short order, if people find it useful. That includes SPDX submission, OSI approval, and then inclusion in Github's licensing apparatus.
Specifically, I'd like to think that corporations would find it significantly more comfortable to use software under LIL than under MIT: They won't have to worry as much about unknown patents held by the authors, and they won't have to worry about future legal disputes with third-party contributors. Both of those are significant issues today — this very week, even.
That said, if you want something permissive, but lawyered-up and bulletproof, use Apache. This isn't intended to compete with Apache. It's intended to compete with what folks actually use and love, which is MIT.