Boston probably just needs to avoid a trade with the White Sox for a starting pitcher
The Chicago White Sox are one of the few surefire sellers at the trade deadline that actually have players worth acquiring. Oakland and Kansas City have been sellers for the last several years and have little left to offer from their rosters. The Rockies have some relievers, but they are not exactly known for their starting pitching prowess especially with what Coors Field does to pitchers.
Given that, one would think that Boston needs to keep the lines of communication open with Chicago. When it comes to bullpen options, that is absolutely true as Keynan Middleton and Kendall Graveman could be excellent additions. However, when it comes to the rotation, the Boston needs to use their resources elsewhere.
Lance Lynn was certainly an interesting candidate. However, he hasn't pitched well in 2023 and with all the money owed to him, it would have been hard to put together a trade package for him without some real concerns that Father Time had finally caught up with him. Fortunately (or unfortunately), the Dodgers took the decision out of Boston's hands as they made the move to acquire Lynn.
As for a guy like Dylan Cease who could be an amazing pickup for Boston who has some team control, the White Sox are all but saying he is untouchable at the deadline this year.
If Chicago changes their tune and makes Cease available, Boston should get in on that action. Otherwise, other teams are going to be more worth their time.