Chelsea have been linked with a world-record bid for Athletic Bilbao goalkeeper Kepa Arrizabalaga with Thibaut Courtois expected to complete a move to LaLiga giants Real Madrid.
And when substitute stopper Green blocked Pape Diop's penalty after four perfect kicks apiece, Eden Hazard was able to confidently stroke home the winning effort to give Sarri a triumphant end to pre-season ahead of the Premier League starting at the weekend.
Marcin Bulka was starting in goal for Chelsea amid the Kepa and Courtois speculation and he made a brilliant save to his left to parry Memphis Depay's powerful drive in the 26th minute.
Depay then slipped Houssem Aouar through on goal with a clever reverse pass but the talented 20-year-old dragged his shot wide of Bulka's far post.
Chelsea struggled to create openings in the first period but Anthony Lopes leapt high to his left to keep out Willian's 25-yard free-kick on the stroke of half-time.
Loftus-Cheek was impressing in midfield with his energy but after the England midfielder raced clear and chipped Lopes the ball bounced back off the face of the post.
Sarri sent on Jorginho and N'Golo Kante and the duo immediately combined to good effect, the World Cup winner sent scampering into the box only to be denied by smart goalkeeping from Lopes.
Green struggled to get close to Lyon's first four penalties but when he guessed correctly and dived to his left against Diop, the former England goalkeeper made a fine save.
And Hazard - wearing the captain's armband after coming off the bench - stepped up to ensure Chelsea warmed up for the start of the Premier League season with a victory.
What does it mean: Blunt Chelsea a worry for Sarri
Lack of goals will be a concern for Sarri heading into the Premier League season. The former Napoli coach has overseen five matches but his new side have only scored three goals. Two of those have come from Pedro, who is far from guaranteed to start most Blues matches. The return of Hazard will help, but Chelsea lack penetration in the penalty area.
Pat on the back: Ampadu takes chance to shine
Chelsea supporters are very excited about Ethan Ampadu and rightly so - the 17-year-old Wales international looks the real deal. There were a couple of moments where he overplayed but the centre-back does not lack confidence and his composure on the ball will be appreciated by Sarri, while he showed bravery in taking a whack on the head from Depay.
Boot up the backside: Drinkwater, Barkley make little impression
Last season's signings of Danny Drinkwater and Ross Barkley seemed strange and neither player found themselves in Antonio Conte's regular plans. Given their chance to shine with Kante and Jorginho on the bench neither midfielder made any real impact on this one, although Barkley's Panenka penalty in the shoot-out was well taken.