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 Wednesday's 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 have fallen at the quarter-final stage in each of the past three seasons since they last lifted the trophy in 2014-15, but with giants Real Madrid and Paris Saint-Germain already eliminated, Ernesto Valverde's side now await 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.
What does it mean? Barca learn their lessons
In the first leg Barca gave an oddly muted performance, but they were closer to their best here and showed a clinical edge to down Lyon despite some nerves. Suarez played a key role in both first-half goals although VAR was used to check if Denayer had fouled him for the penalty.
Valverde's men will take some stopping if they can vanquish their quarter-final demons in the next round. It is the 12th season in a row Barca have reached the last eight, which is a Champions League record.
Barca's captain could not quite match the hat-trick heroics of Cristiano Ronaldo, whose treble helped Juventus knock out Atletico Madrid, but Messi led the way with a typical virtuoso display, which included two goals and two assists.
Not always the most clinical from the spot, Messi showed vast levels of confidence to sit Lopes down with a Panenka and he ran the show throughout, even winning the ball back in his own half on a number of occasions.
+4 - Lionel Messi is the only player in the history of the @ChampionsLeague to score at least 4 goals more than he has conceded (107 goals, 103 goals conceded). Alien. #BarcaOL #UCL pic.twitter.com/DASoL38W0Q— OptaFranz (@OptaFranz) March 13, 2019
Denayer out of his depth
Suarez's quick feet and cunning was too much for Denayer and giving away an early penalty left Lyon with too much to do, as much as Bruno Genesio's men improved after the interval. Denayer was out of position far too often for Lyon.
Key Opta Facts
- Messi has scored two goals and made two assists in a single game for Barcelona for the first time in all competitions.
- He has scored 35-plus goals for Barcelona in each of his last 11 seasons in all competitions (36 goals).
- Barcelona have reached the quarter-finals of the Champions League in the last 12 seasons, the best run of any side.
- Barcelona are unbeaten in their last 30 games at Camp Nou in the Champions League (W27 D3), the best home run of any team.
- Suarez has attempted more shots without a goal than any other player in the Champions League this season (30).
- Coutinho scored his first goal for Barcelona in all competitions since January 30 against Sevilla in the Copa del Rey, ending a run of nine games without a goal.
- Arthur completed 98.6 per cent of his passes against Lyon (71/72), his best passing accuracy in a game for Barcelona in all competitions.