After trading for Victor Martinez on July 31st the Red Sox had 5 players to fit into 4 spots in the lineup - 1B, 3B, C, and DH. Looking at the OPS of each player doesn't suggest that it would be particularly difficult to figure out who should sit:
Kevin Youkilis .987
Victor Martinez .831
Mike Lowell .813
Jason Varitek .755
David Ortiz .713
Defensively the primary alignment is pretty clear as well. With Lowell now a dreadful 3B due to hip surgery and age you put Martinez at 1B, Youkilis at 3B, Varitek at C, and Lowell DH's. Martinez, while not at Youkilis level, is an adequate 1B. Youkilis hasn't played at 3B as well as he did last year, but he is still vastly better than Lowell at this point. Oritz would play roughly 2-3 times a week when Martinez gives Varitek a day off or when Lowell needs a day off to rest his hip (not sure how often this would be required if Lowell is just a DH).
Terry Francona hasn't seen this as such a clear decision. Boston has played 10 games since the Martinez trade, here are how the 39 lineup spots (Casey Kotchman received 1 spot start) have been divided:
Youkilis - 10
Martinez - 10
Ortiz - 8
Varitek - 6
Lowell - 5
Has Ortiz simply been hot and Francona is riding the streak? No, not so much. Ortiz's OPS in August is .339; Lowell's is 1.107. Francona has long been considered to be extremely loyal to his players, at times to a fault. This is one of those 'to a fault' situations - Lowell is by far the better hitter right now.
We don't need to delve into all of Ortiz's numbers they've been well documented. But one that is particularly gruesome is his road OPS which sits at a sickly .594. Seems pretty clear that the best way to put Ortiz in a position where he can succeed is to limit him to playing in Fenway as much as possible. Varitek needs a day off, maybe Lowell sits against a tough RHP - fine play Papi, otherwise no thanks.
Having said all that is it likely that Francona could cost the Red Sox the Wild Card over the lineup? Probably not, even if Big Papi takes all of Lowell's at bats it's unlikely that would cost the Sox even 1 win when looking at earned value. In October though, shouldn't you run out your best lineup whenever possible?