The Dodgers already fleeced the Red Sox for Kiké Hernandez, so there's no sense in LA trying to help out Boston in their sell-high endeavors. The Red Sox are apparently building for the future, so expected them to part with as many rentals as possible. Hernandez was the first to go, and there's speculation Adam Duvall and James Paxton could be next.
Paxton has been good in his 12 starts this year, logging a 6-2 record with a 3.46 ERA, 3.70 FIP, 1.00 WHIP and 75 strikeouts in 65 innings. But don't forget, up until May 12 of this year, the left-hander had made just six starts since the beginning of the 2020 season due to various injuries.
The Dodgers' pitching staff is banged up enough. They don't need to inherit another ticking time bomb liability regardless of the cost. Paxton might only be making $4 million, but you can bet the Red Sox will be looking for a favorable return, which won't be worth it for the Dodgers. His advanced metrics are right in line with his baseline numbers, but this is all about the gamble. How can anybody assume Paxton will maintain his health over the final 2-3 months of the season? He's never made 30 starts in a single campaign and has constantly been hurt ever since the Mariners called him up on a full-time basis back in 2014.
Let somebody else have this be their potential headache. Not worth it for LA.