Indeed. Always friendly to oneself. Giggity goo

This ruling makes no sense to me. The power states that if no friendlies are within 3 the character can use outwit. It goes on to state that the exception to this is if the friendly within 3 has the lost lantern keyword. Where does it state that the character using the outwit must have the lost lantern keyword?

The trouble is that the character is friendly to, and within 3 squares of, itself. As such, if it doesn't have the keyword, it prevents itself from using the power. Slightly strange, certainly, but it is consistent with the rules.

Let's use a different example... only a policeman can use a police car. If a policeman quits the force, he is no longer a policeman so he can no longer use a police car, even if he has before. If he joins the force again, he can use the police car again.

Bringing it back to the topic, substitute "policeman" for "Lost Lantern" and "police car" for "Outwit":
only a Lost Lantern can use Outwit. If a Lost Lantern quits the force (loses the keyword), he is no longer a Lost Lantern so he can no longer use Outwit, even if he has before. If he joins the force again (regains the keyword, he can use Outwit again.

This is correct.

It needs to say "other friendly characters" to exclude the character using/possessing the game effect.