Dye and Ramirez have hit Kazmir this year, and historically Konerko has gotten to him.
Cabrera, Thome, Swisher, AJ, and Anderson (0-6, 5k's) have no chance.
Amongst regulars on the team OPS against LHP:
Dye: .917
Ramirez: .869
Thome: .858
Konerko: .825
Uribe: .790
AJ: .771
Cabrera: .754
Griffey:.649
This doesn't look like a favorable matchup at all.