I'm not ILI, so I'll just go from the ones I know.
One of them is a barrister (court room lawyer), one is doing a PhD in philosophy and intends on becoming an academic and one is in a band with me and has no concrete plans to do anything other than a media degree and be in that band. All three are quite creative people and think well outside the box at times.
I think innovation and creativity are the two big things for ILIs, even if they themselves won't admit it. They can typically pour through large amounts of writing, so things like research, academia and law suit them well. They're kind of like the theoretical to LIE's practical.