The Chicago White Sox has plenty of bats to trade away for experienced veterans.
If the Chicago Cubs acquired Kris Bryant, he would probably have to make a full-time transition to either left or right field. He has played both with the Cubs at times. Yoan Moncada is the full-time third baseman and isn’t going anywhere any time soon. If Bryant came to the Sox, he could play left if Eloy Jimenez makes that transition to DH and he can be the new right fielder if he wanted. His bat and experience would be the biggest thing that the White Sox are acquiring anyway.
In order to get an asset that can hit like that and bring valuable experience, you have to trade away some nice pieces. Zack Collins and Jake Burger are both former first-round picks that haven’t become full-time MLB players yet. Collins has some serious trade value right now as he has been one of the best White Sox players in all of spring training so far. He could be their long-term answer at catcher if they lose Willson Contreras in a trade or free agency.
Jake Burger has dealt with some serious injuries since being drafted but he is still a wildly talented player. He could be a guy who makes it to the big leagues one day because he is such a talented hitter. The White Sox depth chart has filled up since he got hurt so a brighter future might be with someone else.
As for Jimmy Lambert, he is a right-handed pitcher that can help the Cubs pitching depth. Lambert made his MLB debut for the White Sox in 2020. He only appeared in two innings but he didn’t allow a single run, no walks, and only two hits. He had two strikeouts in his one game as well. His ceiling is still to be determined but the Cubs could use as many young arms as possible. If they trade any of their stars, good young pitchers will be on their radar.