Cardinals receive: RHP Lance Lynn
White Sox receive: OF/1B Juan Yepez
Lance Lynn is only a realistic option under a few caveats. First, he would not be their "biggest" pitching acquisition between now and the end of the offseason. He could be a number four starter for the Cardinals, but they'll still be in the market for an ace and another arm to pair with Mikolas.
Second, the cost cannot be expensive. I like the idea of Juan Yepez in a swap because I believe he just needs consistent Major League opportunities to find his way as a hitter in this league. There's a chance that could happen with the Cardinals if they deal off a few young bats, but I think it's much more likely he finds that opportunity elsewhere.
The Cardinals have kind of "air-mailed" their feelings on Yepez to all of baseball with the way they've treated him this year, so he's not going to hold much value in the market since teams know he is expendable for the Cardinals. Why not swap a piece you will not be using long-term to take a flyer on Lynn?
Lynn has a club option at $18 million for 2024. The Cardinals can get Lynn back into their organization for the rest of the year, work with him to see if they can improve his 6.03 ERA to match the kind of strikeout stuff he still has, and if so, pick up his option for next year. If he cannot, they can easily decline the option and they didn't really lose much, or they can try and resign him at a lower number.