We learn two very important things from L.J. Washington. First, there's at least one guy who can totally rock the suit 'n' slippers style. Second, Washington introduces us to the idea of mental divergence.
Here's his spiel in its entirety:
L.J. WASHINGTON: It's a condition of mental divergence. I find myself on the planet Ogo. Part of an intellectual elite preparing to subjugate the barbarian hordes on Pluto. But even though this is a totally convincing reality for me in every way, nevertheless, Ogo is actually a construct of my psyche. I am mentally divergent in that I am escaping certain unnamed realities that plague my life here. When I stop going there, I will be well. Are you also divergent, friend?
That final question haunts Cole, and the audience, for the rest of the film. Is Cole mentally divergent? Is the future of 2035 his Planet Ogo? And if so, what "unnamed realities" have plagued Cole's life so he would invent such a reality? We don't get any answers to these questions, and the film offers us enough evidence to craft multiple, conflicting readings.
As for Washington, he disappears from the film once he plants that seed of doubt in our minds. We don't hold it against him though, as it makes Cole's story all the more interesting.
In fact, we'll even wish him the best of luck with those barbarian hordes on Pluto. That sounds like a tough gig.