So the Dodgers were very much in on Cliff Lee before the Mariners traded him to the Rangers.
According to A Source:
The Dodgers counter-proposed several scenarios, one or the other of which included every valued prospect in the Dodgers' minor league system save one, which the source declined to identify. Common sense suggests that lone untouchable prospect probably was Double-A Chattanooga shortstop Dee Gordon, widely considered to be the Dodgers' top prospect.
Dodgers GM Ned Colletti:
"We're still looking to add pitching, either (a starter or reliever). We're getting to a point in the season where if there is an opportunity to improve our club in any way, shape or form, even if it's in a small way, we have to take a look at it. And pitching is always the area in which you're most vulnerable."
Colletti later went on to note that this is the first stretch of the season that all five Dodger starting pitchers have been anything close to consistent.
If the Dodgers wouldn't give up Dee Gordon for Cliff Lee, it's doubtful he'd be part of a package for Oswalt.