Messi opened the scoring from the spot, before Philipe Coutinho doubled their advantage.
Lucas Tousart pulled one back for the visitors, before Messi took the game away from the Ligue 1 side.
The Argentine dazzled defenders with a stunning solo run before squeezing a low shot past substitute goalkeeper Mathieu Gorgelin and then set up late goals for Gerard Pique and Ousmane Dembele.
“We are all very focused for this competition and Leo too, he has had an incredible match.
“It was extraordinary, we dominated the game, we had chances, we scored two goals and we were able to get one more.
“In the second half, Lyon risked more, they pushed us up looking for the 2-1 that got them in the game, but our people in attack have finished solving the result.
“It was a Champions League match and in this type of game it is normal that we have moments of tension and pressure because they tend to be very fair results.
“In the Champions League you cannot relax because 2-0 was not a definitive result,” Valverde told reporters after the match.