Dawid Malan, Tom Curran, Mason Crane and Craig Overton are also included in the 16-man squad, which was released by the England and Wales Cricket Board (ECB) on Monday.
Moeen Ali, Jake Ball, Adil Rashid, Joe Root and Ben Stokes are all rested by England while Tymal Mills is ruled out through a back injury.
Livingstone, 23, is viewed as one of English cricket's most exciting young talents and scored an 83-ball 129 against the tourists for England Lions.
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Crane, a 20-year-old leg-break bowler, played for New South Wales as an overseas player earlier this year.
The three-match T20 series, which follows the Champions Trophy, starts in Southampton on June 21.
Squad: Jonny Bairstow, Sam Billings, Jos Buttler, Mason Crane, Tom Curran, Liam Dawson, Alex Hales, Chris Jordan, Liam Livingstone, Dawid Malan, Eoin Morgan, Craig Overton, Liam Plunkett, Jason Roy, David Willey, Mark Wood.
(Reporting by Neil Robinson; Editing by Clare Fallon)
