In 2010 and 2011, LHH hit .293 off of Okajima. And if you think that's because he was having a bad year last year, it's not. Lefties hit .364 off of him this year so far.
Oki was a complete waste of a roster spot. Francona had no confidence to use him. He wasn't effective against left handed hitters. There was zero reason to keep him when you've got an option to get a guy who has held lefties to a .185 BAA in his career.
Combine Morales with Hill and we've got two lefties who are going to be really good options in tight games when guys like Granderson, Cano, etc are up to hit.