From the perspective of the general public, Green Lantern is probably the most mysterious member of the Justice League because he's always up in space.
Like with Superman or Flash, you see them basically every day just rescuing cats out of trees or helping old ladies cross the road. Even if you don't live in Metropolis or Central City, you can easily find interviews those heroes have done with famous journalists like Lois Lane or Iris West, or the races they've competed against each other in to raise money for charity.
It's much the same with the other heroes of the Justice League. Wonder Woman is always doing diplomatic work whenever she's not being a superhero. Captain Marvel will just hang out at the Fawcett City Zoo and chat with kids. Even Batman is a known quantity, albeit insofar as that everyone knows that he is a scary mfer who beats Gotham's criminals senseless every night.
But Green Lantern? Sure, he's most often seen in Coast City, but only like three or four times a month. Sometimes, weeks will go by in between sightings of the guy. Honestly, you're more likely to get help from the other local hero, Air Wave.
Most of what people even know about Green Lantern comes from his fellow Justice League members, rather than from the mouth of the man himself. According to their press briefings, he's the protector of the entire space sector that Earth is in. Supposedly, he spends most of his time making sure there aren't more tragedies like what happened to Martian Manhunter's people or Superman's home planet.
