In the shoot-out, both sides converted their opening five penalties before Liedson blazed over Sporting's sixth, leaving Paul McGowan to fire home the winning effort.
The occasion marked the first time a football match had been held at Fenway Park - the historic home of the Boston Red Sox baseball team - since 1968.
Meanwhile, midfielder Juarez faces a race against time as he bids to face Braga in next week's Champions League qualifier.
The 22-year-old met his new team-mates in Seattle on Sunday but is now back in Mexico attempting to negotiate the red tape that will allow him to jet into Glasgow next week.
"Juarez is back home to sort out paperwork, his visa and his work permit," explained Lennon.
"We're trying to rush that through and hopefully he'll be with us early next week and he will be in squad for Braga.
"He made a really good initial impression. His English is quite good which helps.
"We're excited about him and we're hoping he is as well.
"He's young too and if he does well there will be a re-sale value, although we want him to stay as long as he wants at the club and hopefully he will be a big player for us.
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