Lillibridge, 28, was 11-for-63 (.175) in 49 games with Chicago this season. He split time at first base, third base, left field and center field.
"That's why I think I've been in the big leagues as long as I have, just being able to play the places I've been able to do, outfield, infield all that stuff," he said. "Hopefully that can help get me in the lineup here, too, but for the most part, I don't really have any expectations other than just being part of this team and helping us try to win and moving on past the White Sox."
Lillibridge is a career .237 hitter against left-handers. That statistic caught the eye of Red Sox manager Bobby Valentine.
"He looks like he could be a real contributing factor on a winning team," Valentine said. "He played well last year. And he's hit well against left-handers in his career, very well."
While most Red Sox fans might not have seen Lillibridge play, he turned heads last April 26 with a pair of game-saving catches in right field vs. the Yankees.
In the bottom of the ninth, Lillibridge made a leaping catch at the wall to rob Alex Rodriguez of a hit that could have driven in the tying run. He followed with a diving catch to end the game on line drive by Robinson Cano.
"I guess it ranks pretty well here with everyone who doesn't like the Yankees," Lillibridge said. "It's cool, it was a lot of fun. ... But got to make catches, make plays now that I'm here as a Red Sox. I look forward to it."
Lillibridge also has some family ties to New England. His father's side hails from Rhode Island.
"Growing up, my family were huge Red Sox fans, a lot of people from the New England area, Rhode Island, so my dad is pretty excited," he said.