The Victorian right-hander has been in outstanding limited-overs form with 285 runs at an average of 142.5 and a strike-rate of 115.85 for the Melbourne Renegades in the Big Bash League.
White was the domestic one-day tournament's top-scorer last season with 457 runs at 76.16, including two hundreds and two fifties.
He has played four Tests, 88 ODIs and 47 Twenty20 internationals and replaces big-hitting Lynn who was ruled out with a calf problem.
"Cameron's in very good form, as his figures demonstrate. He's playing very well," chief selector Trevor Hohns said.
"He's one of the leading run-scorers in this season's BBL, he's experienced, he's a very smart cricketer and he's a good fielder. He ticks all the boxes for what we need at this stage."
The opening match of the five-game series takes place at the Melbourne Cricket Ground on Sunday.