Two possibilities I've heard discussed:

Libby had a loved one killed in Hurley's "accident" and flipped out about it and that's how she ended up in the institute. She then recognized Hurley in the institute and later when he won the lottery and started stalking him.

Libby knows Hurley won the lottery and is only after his money.

Personally, I don't like either of these scenarios. Hurley is one of my favorite characters and I would love him to be able to get the girl just for himself - not because he's rich or to get revenge.

Here's what I think. I don't know why Libby was in the institution to begin with or why she was in Australia, but she recognizes Hurley and claims to be a psychologist since it's the opposite of a crazy person and she's probably pretty familiar with the lingo from being a patient and thinks she could pull it off. She didn't really do much to Claire to "help" her - just had her relax and she even seemed kind of freaked out when it worked and Claire started remembering things. Also, she would have told Hurley about being a psychologist when he was having his episode on the cliff and offered to help somehow. She genuinely likes Hurley, but doesn't want him to know her secret.

Then again, she could be an Other. That's the beauty of this show - no character is all good or all bad.