Look at their career stats and Konerko is slightly better. I see someone posted their career stats but failed to mention who was who.
AB Ave. Hr RBI OBP.
Konerko 4165 .280 222 730 .351
Lee 4127 .276 211 636 .364

Now looking at this and the fact Konerko is a year younger and not injured for 3 months, why would there be a problem making this deal? I'm not sure the team getting Lee would not be getting the worst of the trade. Will his injury effect his swing in the future? Will it be a chronic pain problem in the future? Granted he had a career year, but how many times have we seen players do this? Perfect example is Seattle 3b Andie Beltre.