Dutch championship runners-up PSV took the lead against competition debutants Waregem with a stunning 30-metre strike from Memphis Depay just after the hour before substitute Jurgen Locadia added a second in the 75th minute for the 1988 European Cup winners, who also hit the woodwork four times.
While PSV are aiming for their first group stage appearance since the 2008/09 season, Lyon have had more success in recent years having reached the semi-finals in 2010 and they gave themselves the narrowest advantage to take into the second leg against Grasshoppers when Milan Bisevac headed the only goal after 64 minutes.
The Serbian defender's powerful header flashed past goalkeeper Roman Burki from Clement Grenier's free kick but Michael Skibbe's Zurich-based side will feel hard done by having twice hit the post in the first half at Stade Gerland.
Luciano Spalletti's Zenit St Petersburg also have a 1-0 lead over Danish side FC Nordsjlland thanks to Aleksandr Kerzhakov, who scored four minutes after coming on to secure victory away to opponents who were also in the group stage last season.
Former European champions Steaua Bucharest claimed a 2-0 win over Georgian side Dinamo Tbilisi with two goals from teenager Gabriel Iancu.
The Romanian champions had goalkeeper Ciprian Tatarusanu to thank for saving a Xisco penalty just after the hour before halftime substitute Iancu struck in the 64th and 80th minutes.
Last season's Europa League semi-finalists Basel earned a 1-0 win over Maccabi Tel Aviv thanks to a 39th-minute strike from Valentin Stocker.
The Swiss champions dominated the match but could not add to the goal from 24-year-old Stocker who fired a low shot past goalkeeper Juan Pablo.
Austrian champions Austria Vienna, who like Basel entered the qualifiers in the third round, also have a narrow 1-0 lead to take into their second leg against FH Hafnarfjordur of Iceland after winger Daniel Royer scored in the 25th minute.
Marian Cisovsky's hat-trick helped Czech champions Viktoria Plzen win 4-0 against Estonia's JK Nomme Kalju, who had celebrated their first win in Europe in the last round when they beat HJK Helsinki.
Plzen, who also scored four first-leg goals in the last round against FK Zeljeznicar, opened the scoring after two minutes in Tallinn through Cisovsky who added two more in the second half either side of Michal Duris's 77th-minute strike.
Croatia champions Dinamo Zagreb grabbed a last-minute goal from substitute Ante Rukavina to secure a 1-0 win against FC Sheriff of Moldova having controlled the game against the visitors and struck the woodwork through Junior Fernandes while Metalist Kharkiv's Marko Devic scored in each half for the Ukrainians to wrap up a 2-0 win over PAOK in Salonika.
Kazakhstan champions FC Shakhter Karagandy thrashed Albania's KS Skenderbeua 3-0 with goals from Aldin Dzidic, Roman Murtazayev and Sergei Khizhnichenko securing victory at the Astana Arena.
The hosts also beat last season's group stage contenders BATE Borisov in both legs of their second qualifying round tie.
There are five more third qualifying round matches scheduled for Wednesday with the return legs on August 6 and 7.
The winners of the qualifiers will reach the play-off round which offers a route into the lucrative group stage.
Third qualifying round (first leg) results
Lyon (France) - Grasshoppers (Switzerland) 1-0 (half-time: 0-0)
Dinamo Zagreb (Croatia) - Sheriff Tiraspol (Moldova) 1-0 (half-time: 0-0)
PSV Eindhoven (Netherlands) - Zulte Waregem (Belgium) 2-0 (half-time: 0-0)
PAOK Salonika (Greece) - Metalist Kharkiv (Ukraine) 0-2 (half-time: 0-1)
Basel (Switzerland) - Maccabi Tel Aviv (Israel) 1-0 (half-time: 1-0)
Nordsjaelland (Denmark) - Zenit St Petersburg (Russia) 0-1 (half-time: 0-0)
Austria Vienna (Austria) - FH (Iceland) 1-0 (half-time: 1-0)
Dynamo Tbilisi (Georgia) - Steaua Bucharest (Romania) 0-2 (half-time: 0-0)
Kalju Nomme (Estonia) - Viktoria Plzen (Czech Republic) 0-4 (half-time: 0-1)
Shakhtyor IK (Kazakhstan) - Skenderbeu (Albania) 3-0 (half-time: 1-0)