White, who flew out last week as an injury replacement, features in the back row alongside Welsh pair Martyn Williams and Michael Owen.
Williams is among four players in the Lions 22 beaten 48-18 by the All Blacks on Saturday involved in the trip's final midweek encounter.
He is joined by scrum-half Matt Dawson, who starts, together with bench men Martin Corry and Shane Horgan.
The side to face Auckland suggests that Lions head coach Sir Clive Woodward is unlikely to tinker with his Test team for next weekend's third and final game, although injuries to Jonny Wilkinson and Gavin Henson could yet force his hand.
Scotland hooker Gordon Bulloch, who some will consider unlucky to have missed out on Test recognition so far, will again captain the midweek team.
British & Irish Lions team to play Auckland at Eden Park on Tuesday:
G Murphy (Leicester and Ireland); M Cueto (Sale Sharks and England), W Greenwood (Harlequins and England), G D'Arcy (Leinster and Ireland), D Hickie (Leinster and Ireland); C Hodgson (Sale Sharks and England), M Dawson (Wasps and England); A Sheridan (Sale Sharks and England), G Bulloch (Glasgow and Scotland, captain), J Hayes (Munster and Ireland), S Shaw (Wasps and England), B Kay (Leicester and England), J White (Sale Sharks and Scotland), M Williams (Cardiff Blues and Wales), M Owen (Newport Gwent Dragons and Wales).
Replacements: A Titterrell (Sale Sharks and England), M Stevens (Bath and England), B Cockbain (Neath-Swansea Ospreys and Wales), M Corry (Leicester and England), C Cusiter (Borders and Scotland), R O'Gara (Munster and Ireland), S Horgan (Leinster and Ireland).