Lexie Grey is the daughter of Thatcher and Susan Grey (who passed away at the end of Season 3), and thus the younger half-sister of Meredith Grey. She also has a younger sister, Molly Grey Thompson.
Lexie is a graduate of Harvard Medical School.
At the end of Season 3 of Grey's Anatomy we learn that Lexie Grey will be a new intern at Seattle Grace. She was introduced in the penultimate episode of the third season as a woman Derek Shepherd met at the Emerald City Bar.
In the season finale, Derek confessed to Meredith that he met another woman (although he still doesn't specify who) and when she asks if she should be worried, he confirms her fears. While he didn't get together with Lexie, Derek admits meeting her was the highlight of his day.
Lexie Grey later made her first appearance in Seattle Grace when she introduced herself to George O'Malley, who was cleaning out his locker as she was on her way in. Upon hearing the name Lexie Grey, George clearly realized her connection to Meredith. What's to come of this new intern?
Izzie: They tried number 9? Who does 9?
Sadie: Well personally I'm a fan of 5, 7, 8, pretty much 12 through 20.
Meredith (laughs): I would try 15.
Izzie: Don't. Don't try 15. I would try 16. Yeah. I've never done that before.
Alex: You'd try 16?
Izzie: Uh huh. I would. I totally would. (Izzie and Alex look at each other then quickly leave the table)
Lexie: Um, don't do 16 too fast. It can hurt badly ... I heard.
Lexie: Wait, what's the prize?
Chief: You get to scrub in on Shepherd's craniotomy.
Chief: And hold the doomsday sucker.
Lexie: What's the doomsday sucker?
Izzie: Doomsday sucker?
Chief: It's just a really big sucker.