The Reds had lost three and drawn one of their last four matches ahead of Wednesday evening's clash, but they looked a lot brighter at the Stade de Geneve as a number of their key men returned to action.
Alisson was guilty of a howler inside the first few minutes to gift Lyon an early advantage, though Liverpool responded well to take a 2-1 lead into the break and Harry Wilson added a fine third goal after the restart.
One of Liverpool's returning players made a disastrous start to the match as Alisson failed to bring Memphis Depay's hopeless pass under control in the box and fouled Moussa Dembele once the striker had pounced on the loose ball.
Depay made no mistake from the penalty spot as Lyon, 2-1 winners over Arsenal at the Emirates Stadium on Sunday, punished the Brazilian's rustiness.
Liverpool hit the post through a deflected Wilson cross a few minutes later, but it was the French side who were looking the more likely to score on the counter as Dembele tested Alisson down low.
The Reds soon took control of the match, however, with Firmino firing past Lopes on the turn after Thiago Mendes failed to deal with Shaqiri's cross.
Four minutes later Klopp's men were in front thanks to a comical own goal from Joachim Andersen, who shinned Ki-Jana Hoever's cross into the top corner under little pressure from the edge of the six-yard box.
Salah and Wilson both came close with their shots late in the first half, and it did not take long into the second period for Liverpool to bag their third.
Half-time substitute Bobby Duncan had an angled drive kept out down low, but he teed up Wilson to score the goal of the game 53 minutes in - the Welshman picking out the top corner from around 27 yards out.
A glorious chance for Bertrand Traore to reduce the arrears then went begging when he failed to beat Alisson from a one-on-one position.
Young signing Harvey Elliott was among the Liverpool players to be introduced in the second half and he had a powerful shot kept out in the most promising of his moments on the ball.
Liverpool should have added to their tally, with Jordan Henderson also wasting a promising opportunity, but a return to winning ways was the most important thing for Klopp ahead of Sunday's Community Shield clash with Manchester City.
LYON (4-3-3): Lopes (Tatarusanu 46'); Dubois (Tete 63'), Andersen (Solet 65'), Denayer (Marcelo 46'), Marcal (Rafael 22'); Lucas (Diop 46'), Mendes (Tousart 46'), Aouar (Fofana 75'); Traore (Kitala 63'), Dembele (Gouiri 65'), Depay (Caqueret 63')
LIVERPOOL (4-3-3): Alisson (Mignolet 62'); Hoever (Van den Berg 46'; Van Dijk 62'), Gomez (Alexander-Arnold 62'), Lovren (Matip 62'), Larouci (Robertson 62'); Shaqiri (Milner 31'; Henderson 62'), Lallana (Fabinho 62'), Keita (Lewis 46'; Wijnaldum 62'); Salah (Duncan 46'; Elliott 62'), Firmino (Brewster 31'; Origi 62'), Wilson (Oxlade-Chamberlain 62')body check tags ::