The 34-year-old White has not represented Australia in any format since 2015.
The right-hander has been in strong Twenty20 form with 285 runs at an average of 142.5 and a strike-rate of 115.85 for the Melbourne Renegades in the current Big Bash League.
While he plays predominantly as an opener domestically, White is expected to fill the vacant No.4 position in the batting order. Lynn has a calf injury.
Australia plays England on Sunday at the Melbourne Cricket Ground to open the series.
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