Thatcher Grey is the father of both Meredith and Lexie Grey. When Meredith's mother had an affair with Richard Webber, Chief of Surgery, her father left them. I think Meredith was 6 when he left. He left them and started a new family with a new wife. That' s where Lexie comes in. After Meredith's mother dies, Thatcher's new wife tries really hard to mend the relationship between the father-daughter. Things start out well, but when step-mom comes into the E.R. with hiccups, everything goes very badly. Meredith recommends a simple surgery to correct the problem and there are complications leading to her death. Thatcher can't forgive Meredith for that and is a lousy alchoholic to boot. Lexie can't live with him after it all. It's too hard to live with him while he's drinking and that's why she moved out of the house. Not a regular on the show, he's made many appearances to change things up over the last two seasons.

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Thatcher Grey in the E.R. (episode 8)