Daisuke Matsuzaka, who went 18-3 with a 2.90 ERA, is slated for Game 2, on Friday.
"I think Beckett was probably an obvious choice to throw Game 1," said Francona. "On Friday, in his side session, he strained his oblique. We'll pitch those two guys and slot him in Sunday, and hopefully, be rolling. That's the whole idea."
Oblique injuries are among the hardest to predict. So while the Red Sox are hopeful that Beckett can pitch Game 3, they will continue to monitor the situation. If all goes well, Beckett will throw a side session on Thursday in Anaheim.
"Certainly, if it goes the wrong way, we're going to use -- hopefully -- very good judgment," said Francona. "I think we're slotting him in there because we think he can pitch there. [Game 2] was actually discussed. I think after [general manager] Theo [Epstein] and I, and [pitching coach] John Farrell talked about it more and more and more, we thought that was pushing it, because then you're messing around with maybe cutting short a side session or not having enough throwing.
"It's not just health, but it's competing also. He has to be able to go out there and execute his pitches. I think he's going to be OK."
Statistically speaking, Lester and Matsuzaka both had better seasons than Beckett, who battled right elbow problems at times and went 12-10 with a 4.03 ERA. But Beckett finished the season strong and seemed primed and ready to lead the Red Sox into the postseason, where he has been a force in his career.
But the right-hander's ill-fated bullpen session changed things.
"It was on his 40th pitch," Francona said. "He was almost done. And again, I don't think it was something where he threw it and grabbed it. It was almost between pitches and he took a deep breath and he was, like, 'I feel something,' so he stopped. He went out and got treatment. They've been working on him. Initially, when you hear something like that, you're kind of like, '[Oh, no].' But Dr. Gill came in and said, 'Relax, this is going to be all right.' That was kind of reassuring."
Beckett's issue is the latest injury setback for the Red Sox, who have recently been in limbo with regard to third baseman Mike Lowell (right hip) and right fielder J.D. Drew (bad back). In fact, dating back to when Curt Schilling got injured before Spring Training and missed the entire season, health woes have been a constant theme for a team that still managed to win 95 games and win the AL Wild Card.
"I don't think it's frustrating," Francona said. "Things happen and you deal with them, and if you deal with them well enough, you handle it. If you don't, you go home. Things happen, and you have to deal with them and find a way to win. I think Lester and Daisuke will do just fine."
If Beckett is unable to pitch Game 3, veteran knuckleballer Tim Wakefield would be the likely choice to get the ball.
Beckett was unavailable for comment on Sunday, and Lester declined to speak with reporters.