Things started to move very fast for this couple. Mark decided that he wanted Lexie move in with him. She resisted at first, but was eventfully convinced after being reassured by Mark's friends. Things were going well for the two of them until a girl claiming to be Mark's daughter popped up. It turned out she was in fact Mark's daughter, she was pregnant, and had nowhere to go. Mark told her she was welcome to stay with him and Lexie if she wanted. This didn't go over too well with Lexie. She was angry Mark hadn't consulted her about this, and heck, she didn't even really like the girl. That was the end of this portion of Mark and Lexie's relationship. Lexie left and moved in with Derek and Meredith.
These two were just biding their time with other people until they could get back together. Lexie rekindled her 'relationship' with Alex. Mark made himself available to various members of the staff.