Lyon were in cruise control with a 3-0 lead courtesy of goals from Lucas Paqueta in the ninth minute, Houssem Aouar after 28 minutes and a penalty from Memphis Depay just before the half-time break.
Paqueta, 23, had earlier arrived in the city to undergo a medical. Capped 11 times by Brazil, he joined Milan from Flamengo in January last year but failed to properly settle at San Siro.
Milan, who dropped to 14th in Serie A at one point this season, have lost only twice since the start of the year and climbed to sixth, putting them on course for a Europa League place which has become their target for this season.
Coppa Italia: Paulo Dybala scores brace in Juventus win; 10-man Fiorentina beat Atlanta to set up Inter Milan clash
Dybala and Gonzalo Higuaín combined for the opening goal in the 16th minute, exchanging a series of passes before Higuaín finished it off
Philippe Coutinho scored one goal and helped set up another as Brazil beat South Korea 3-0 in a friendly on Tuesday to give the five-time world champion its first win in six games.
Serie A: Paulo Dybala's second-half strike helps Juventus beat AC Milan; Lazio and Cagliari move into top four
Paulo Dybala struck the decisive goal in Juventus' 1-0 win over AC Milan on Sunday after replacing Cristiano Ronaldo as Juventus stayed top of Serie A, while Lazio and Cagliari moved into the Champions League places.
International friendlies: Brazil denied victory by determined Panama as injured talisman Neymar watches from stands
"The performance wasn't brilliant but it wasn't below par either," Brazil coach Tite said. "When we go to the Copa America we will make more accurate choices to be more efficient."
Serie A: Bologna stun Inter to increase pressure on Luciano Spalletti; Nicolo Zaniolo rescues point for AS Roma against AC Milan
Federico Santander scored the winner as Bologna stunned Inter Milan to pile the pressure on Luciano Spalletti as Roma rescued a point against AC Milan.
Serie A: Big guns Juventus, AS Roma, Inter Milan hope to get back to winning ways after crashing out of Coppa Italia
The big guns all suffered upsets with Juventus crashing 3-0 to Atalanta, Napoli falling 2-0 to AC Milan and Roma suffering a 7-1 humiliation at Fiorentina.
Barcelona lead the way in January transfer window as Premier League clubs make no major signings on deadline day
While the window was relatively quiet in England, some of Europe's biggest names made moves, mostly well before deadline day, with Barcelona leading the way.
Coppa Italia: Juventus, AC Milan book quarter-final spots; anti-Semitic chants mar Lazio's thrashing of Novara
Lazio dismissed racist and anti-Semitic chanting during their Coppa Italia tie as a 'psychosis focusing on a minority or non-existent incidents'.
Serie A: Brazilian midfielder Lucas Paqueta arrives in Italy ahead of record transfer move to AC Milan
AC Milan are reported to have agreed to a deal with Flamengo — the club Paqueta joined as a ten-year-old — in what would be the most expensive signing of a Brazilian by an Italian club.
Serie A: AC Milan agree deal to sign Lucas Paqueta, considering swoop for Zlatan Ibrahimovic, says director Leonardo
AC Milan has reached an agreement with Brazilian club Flamengo to sign highly rated Lucas Paqueta, and are considering a swoop for Zlatan Ibrahimovic in the future.