Inspired by Joseph's comment to my regurgitation of the oft-professed comment that Detroit would be seeking to add a LH bat, I looked up a few things. Here's what I found (Tigers AL rank vs. RH/LH) :
Runs : 3 vs RH / 12 vs LH
OPS : 5 vs RH / 12 vs LH
BA : 6 vs RH / 12 vs LH
OB: 9 vs RH / 13 vs LH
SLG: 3 vs RH / 10 vs LH
I can see the TIgers looking to add a bat (supplementing Monroe or Inge) but I would hesitate if I were them (if one person can actually BE the Tigers - besides AL Kaline that is) of putting any stipulation on the side of the plate the dude swings from. In fact, I'd lean heavily towards someone that shows they can get on base vs. a decent lefty.
Based on living in Toledo-area since 1989, the Tigers have grown to be solidly my 2nd favorite team due to the exposure the Mud Hens gave provided to me of the future TIgers. I know I had on the surface thought "Yeah, they don't have much from the LH side besides Guillen switching and DaMeat coming back" but closer investigation shows their concerns should lie elsewhere, or at least not so specifically on a LH hitter.