After last month's goalless first leg, Messi opened the scoring at Camp Nou from the penalty spot, with Philippe Coutinho adding a second prior to half-time in Thursday's (NZDT) tie.
Although Lucas Tousart sparked hope of a second-half Lyon fightback, Barca held their nerve and Messi struck again before Gerard Pique and substitute Ousmane Dembele wrapped up the scoring to seal a place in the last eight, where a bigger test likely awaits.
Barca has fallen at the quarter-final stage in each of the past three seasons since they last lifted the trophy in 2014-15, but with giant Real Madrid and Paris Saint-Germain already eliminated, Ernesto Valverde's side now awaits Friday's draw with interest.
Anthony Lopes made a brilliant early save to deny Messi but Barca's captain beat him from 12 yards in the 17th minute.
Jason Denayer clumsily tripped Luis Suarez in the box and Messi, who had nine attempts but only one on target in the first leg, beat Lopes with a brilliant Panenka.
Moussa Dembele's drive deflected narrowly wide but Barca soon extended their lead.
Arthur's superb pass found Suarez and he jinked easily through the Lyon defence to square for Coutinho to tap in before a tearful Lopes had to make way due to a head injury.
Marcal cleared Messi's delicate chip off the line after the restart but Lyon gave themselves hope by grabbing a goal back in the 58th minute.
After a spell of head tennis in the Barca box, Tousart controlled the ball and sent a low volley flying past Marc-Andre ter Stegen, with the goal standing after a lengthy VAR review.
Lyon grew in confidence but they were caught out at the back with 12 minutes to go, Messi dazzling defenders before squeezing a low shot past Mathieu Gorgelin.
And the substitute goalkeeper was then beaten again twice as Barca picked Lyon off on the break, Messi sensationally setting up Pique and Dembele for further goals.