'Would You Fight For My Love?' is the new single from solo album 'Lazaretto'
Pete Doherty had mentioned possibility of collaboration
Picture was posted via Third Man Records' Instagram account
The White Stripes had previously covered the same song
The 'Alone In My Home' and 'Entitlement' demos came out as part of Third Man Records' Vault service
Sales of 60,00 make White's second solo LP best-seller since Pearl Jam's 'Vitalogy'
The singer played at Detroit's Masonic Temple venue he saved from closure last year
Detroit born singer returns home to join in game against Chicago White Sox
The pair performed 'Loser' and 'Pay No Mind' together
Musician invited by local baseball team to start game against Chicago White Sox on July 29
The White Stripes man played the song during a three-hour gig in Chicago
White also covered Lorde's 'Royals' during gig in Milwaukee on Monday night (July 21)
The singer mashed up the song with The White Stripes' 'Icky Thump' in Louisville
Foals, Royal Blood and Lykke Li also play the third day of the event in Poland
The former White Stripes man played an immersive show in an office block
White played set for Zane Lowe's BBC Radio 1 show last night
Instrumental tribute came at recent gig in Dublin
US musician plays set covering many of his former bands plus new solo album 'Lazaretto'