It would be nice to pick up every available player that could upgrade a position (like Center), but that's just not realistic. That's why they have a cap, and that means teams have to prioritize positions.
Snead said some years ago that his analysis is that you can pick up good Olinemen in the middle rounds of the draft and develop them, and they can be every bit as good as the higher picks. And, of course, you can pick up younger guys that were cut or on someone's PS if you have a book on them that says they can be developed.
Obviously the Rams are willing to spend some money on LT.
But it also makes me think that the Rams may have their eye on a couple of Centers they like in the draft, as well. Getting Blythe back for not too much to give a rookie time to develop could be in the plan.