After watching "Meet Kevin Johnson" yet again, I am not convinced that Libby's appearance in Michael's hospital room took place during his flashback after he tried to kill himself. It's a stretch, but plausible...
In Season 1, we witnessed Michael getting hit by a car, and he was in the hospital for an undisclosed amount of time. Back then, Libby was alive and well. Before she became a clinical psychologist, she took one year of medical school (she also tended to the wounded after the Tail Section crashed). I'm not exactly sure about the year, but she very well could have been working at the hospital where Michael was during that time.
The producers intermingled flashbacks with flash forwards during the previous episode (Jin and Sun, respectively), so who's to say that they didn't interject a true flashback again? We know that Michael has been in the hospital twice due to injuries sustained by a car, and it can't be coincidence that Libby has medical training. Why else mention it during her brief stint on the island?
Obviously, when Libby shows up on the freighter as Michael is about to set off Ben's bomb, that was an apparition (or a Smoke Monster manifestation, etc.).
I have always enjoyed her character on Lost, because let's face it - we have no idea is she was truly mentally ill or merely had a twin sister.
To me, the most pivotal Libby scene in Lost history took place in Season 2, moments after she convinced Hurley not to dive into the ocean after his imaginary friend Dave. The look on her face after he asks her if she thinks he's capable of change is priceless (see photo below). Her expression goes from real affection to absolute misery in a millisecond, and I believe it was very telling.
Here are the many faces of Libby and/or Elizabeth, in reverse order:
Mental patient Libby
Post those theories below!