Lee has been progressing so well that he's already hitting in the batting cage, and on Tuesday the first baseman fielded ground balls during batting practice and was throwing to bases. Lee worked out at a health club Monday with strength and conditioning coach Gene Coleman.
"I think the big part is running," Lee said. "I ran on Sunday and felt OK, but I didn't push it. I ran at about 60 percent and felt OK."
Mills said Lee would run again on Wednesday before being sent out for a couple of days on a rehab assignment. Lee is eligible to come off the DL for Sunday's game against the Rangers in Arlington.
"I definitely have to go," Lee said of a rehab assignment. "I have to be in a real game and push it a little bit and see how it responds."