Barcelona had 25 shots against Lyon but were unable to find the net as they drew 0-0 against the French side in the Champions League on Tuesday.
Lyon also had their moments -- Marc-Andre ter Stegen made two unbelievable saves -- but Barca will feel they missed an opportunity to edge ahead in the last 16 tie.
The two teams will meet again at Camp Nou in the second leg next month (March 13).
A fast and furious start saw Ousmane Dembele fire wide before Lionel Messi sent a free kick over teh bar.
Ter Stegen then stepped forward to keep out Houssem Auoar before tipping a brilliant Martin Terrier effort on to the bar as the home team showed signs of their quality.
Dembele, Messi, Ivan Rakitic and even Sergio Busquets also had chances before the break but the scoreline remained goalless at half time.
Lyon started the second half well but Barca soon took control of the game, Suarez missing a good chance before Messi saw a shot saved by Anthony Lopes.
Philippe Coutinho replaced Dembele before Suarez wasted Barca's best chance on what was a tough night for the Uruguayan, bending wide from Jordi Alba's cutback.
Coutinho then forced Lopes into a save as Barça tried to force the issue but there was to be no late winner, with Lopes also saving from Busquets.
It's now six games and three years since Barça won away from home in the Champions League knockout rounds -- against Arsenal -- and just as worrying is Suarez's form in Europe.
The striker's without a goal on the road in nearly four years. There have been 25 hours of match action since he last bagged an away goal, against Roma in 2015.