The bonus-point victory keeps the Gauteng side in contention for a knockout berth, though a tough trip to Perpignan in France still awaits.
Winless after the opening two rounds, the Lions needed to show urgency and they struck first, as debutant Batho Hlekani capitalised on loose ball near the line to score in the seventh minute.
Lyon responded when a wayward Lions pass was snapped up by debutant Charly Mignot, who raced clear to score under the posts, but the home side hit back with two tries in quick succession, Richard Kriel finishing off a sweeping backline move before Quan Horn dotted down under the poles following sharp interplay out wide.
Renzo du Plessis also crossed just before the break as the hosts surged into a commanding 28–7 lead, but Lyon managed a late first-half response through Alexandre Tchaptchet, who powered over to cut the deficit to 28–14.
The French side carried that momentum into the second half. Scrumhalf Esteban Gonzalez finished a well-worked move down the left to make it 28–19, before the Lions struck back through Angelo Davids, who finished brilliantly in the corner after a clever kick-and-chase from Smith.
Hooker Mathis Sarragallet scored from the back of a dominant maul as Lyon refused to lie down, and when Alfred Parisien chased down a clever chip to touch down under the posts, Jackson's conversion suddenly brought the visitors to within two points, setting up a tense finale.
With the pressure mounting, the Lions turned to their forwards. After repeated drives close to the line, replacement hooker Morne Brandon powered over from close range in the 78th minute, sealing the contest before Smith added the extras to put the result beyond doubt.