I think people might be underrating Lawrie a bit. He is still only 24 and although he has been viewed as a bit of a disappointment, he is still considered a potential star. As a point of reference, Steamer currently projects him to put up a 4 WAR in 2015. Betts, by comparison (and Steamer is high on him too) only projects to be 2.6 win player.
Beane wanted a trade that would give him some prospects to rebuild his rotation while also replacing his star third basemen with a cheaper, star-potential, alternative. The only way the Sox could have offered a similar package is by including Betts (since Betts could fill the A's other IF hole -2B).
Who knows how aggressively the Sox pursued a Donaldson trade before signing Panda. IMHO a package centered around Betts would have been worth offering, and may have represented a better return than what BB ended up eventually receiving. That said, it's possible that such an offer was made and Beane just isn't as high on Betts as everyone else. We'll probably never know..