That was not before Barca had scored a second as the faultless Arthur Melo played an angled pass into Suarez, who wriggled clear.
At that stage, another goal would have sent Lyon through on away goals, but Barca - or more specifically Messi - stepped things up in the final 12 minutes. "Sometimes he is just unstoppable".
That is likely to cost them at least £8.8m if he makes an early Nou Camp exit.
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Dembele was touch and go for the game after straining his hamstring at the weekend but came on for the final 25 minutes, scoring the final goal in a 5-1 win. Napoli is now second in the Serie A and narrowly failed to qualify for the knockout stages of the Champions League, after finishing behind Liverpool and Paris Saint-Germain in a tough group.
"When he is at that kind of level, he is nearly unstoppable", Lyon coach Bruno Genesio said.
The Turin giants are in the last eight after Tuesday's epic 3-0 win over Atletico Madrid, with Cristiano Ronaldo scoring the hat-trick that enabled them to reverse a 2-0 defeat from the away leg of the last-16 tie.
He combined fluidly with strike partner Luis Suarez and almost put the game to bed at the start of the second half when he beat Lyon substitute keeper Mathieu Gorgelin but saw his shot cleared off the goalline.
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"What Cristiano Ronaldo and Juventus did was impressive", Messi told Marca.
The Premier League might be awakening again as a European force, but Ronaldo and Messi remain the kings of the competition and they should strike fear into the hearts of every English club still dreaming of winning this year's Champions League. He then set up two more goals.
"Sometimes I will see Luis Suarez looking worn out so I will ask the Coach to put me up front, and I think I have the instinct to play in that position more often".
"They'll be two handsome games, we'll have to be very careful, and treat them like we did Atletico".
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She also confirmed that the shooting was a "terrorist attack ". "From what we know, it does appear to have been well planned". Police officers found weapons and improvised explosive devices in the cars of the people arrested.
"We all have to love each other as teammates because we're all looking for a place in the team, but Cristiano won everyone over very quickly".