Messi opened the scoring with a Panenka penalty and, after Lucas Tousart sparked Barca nerves by making it 2-1, the Argentine star took the game away from the Ligue 1 side on Wednesday.
The Barca captain dazzled defenders with a stunning solo run before squeezing a low shot past substitute goalkeeper Mathieu Gorgelin.
And Messi then set up late goals for Gerard Pique and Ousmane Dembele to end the second leg with two goals and two assists at Camp Nou.
"We are all very focused for this competition and Leo too, he has had an incredible match," Valverde said midweek.
"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."
Despite Lyon's attempted fightback, Barcelona booked a place in the quarter-finals of the Champions League for the 12th year in a row.
But Barca have exited in the quarters three seasons in succession and Valverde has no preference over who the La Liga leaders face in the next round.
"It is impossible to look only at one team," Valverde said of the draw.
"We have all made merits to progress, we will see the rival, any one that we meet will be complicated."