The Red Sox are currently taking offers for both Lester & Andrew Miller. I'd be surprised if Miller wasn't traded. I also expect the Sox to unload some of their position players. As for Lester, my personal opinion is that he'll get traded. Likely to a National League team, possibly the Dodgers or Cardinals.
If you're Jon Lester, do you really want to remain in Boston?? This is a team going nowhere and will likely be battling to stay out of the AL basement next season also. This is one of the rare teams in the AL East that hasn't had many injuries this season as compared to the likes of New York, Toronto and Tampa. Baltimore is also a team that hasn't had many injuries, the only one i can think of being to catcher Matt Wieters. Basically, the Red Sox have played with the same core group of players that they had last season when they had everything going their way & surprisingly winding up winning the World Series under a very average manager in John Farrell. Everything went their way, they got all the bounces, and shocked everyone (probably themselves). Okay, they lost Jacoby Ellsbury, but that's their own fault. He's also had a very average season playing for the Yankees.
This reminds me of a book i read decades ago called "Number 1", written by Billy Martin (and co-written by Peter Golenbock if i remember correctly). Early in the book, Martin talked about his days managing the Detroit Tigers. That was a couple of years after they had won the World Series in 1968. He mentionned that it was the same old bunch that had won the championship and in their minds, they still believed that they were the best team in baseball. He mentionned that teams who keep basically the same core of players after a championship will usually fade the year after since the players aren't as hungry to win. They get in that zone where they believe that they are still the best and falsely believe that they don't have to push themselves anymore in order to win, which is why successful teams (dynasties) will usually replace several of those players the following year. They want to keep the players hungry to win.
If i'm the Red Sox, i'm also trading the likes of Pappi and maybe even Pedroia. They'll get very good value for them and Pappi's best years are long gone. He's also just a DH and they come a dime a dozen. He doesn't have many years left and i also believe Pedroia's best years are behind him.