Lee, who's staying the Astros at their hotel in Dallas because Corpus Christi is playing in nearby Frisco, is scheduled to play Friday and Saturday for the Hooks and should be activated Sunday if all goes well.
Meanwhile, a trio of other players is progressing from various injuries.
Shortstop Marwin Gonzalez, who's been out since June 7 with a bruised right heel, took swings off a tee for the first time Friday and expects to be able to play in a week.
"It still hurt, but I'm getting better every day," he said. "I was still a little sore, but I hope to be OK in one week."
Outfielder Travis Buck is making progress from the right Achilles' tendinitis that's kept him in the shelf since May 29, and outfielder Fernando Martinez is scheduled to go through more tests next week in Houston to gauge his health. He went on the 7-day DL on Saturday with post-concussion syndrome.
"If he comes through OK, he might be ready to start here pretty quick on a rehab assignment by the end of [next] week," manager Brad Mills said. "The guys are coming around and hopefully we're getting healthy and going to get guys back again."