The Lyonnais, who had taken the advantage after being down by 23 points, finally lost to a drop 5 minutes after the siren.
In bad shape in the Top 14, Lyon began its journey in the Champions Cup with a defeat (36-34) on the Bristol pitch on Saturday evening, but still left with an offensive bonus point and a defensive bonus point.
With several executives left to rest, starting with the second row Romain Taofifenua and the scrum half Baptiste Couilloud, the Lyonnais believed in the perfect move by taking the advantage in the 77th minute after a try from center Alfred Parisien.
But the Bristol players, who led by 23 points before letting LOU come back, finally won thanks to a drop from their opener Callum Sheedy after the siren.
With a fifth defeat in its last six matches, Lyon remains in doubt before hosting the South African franchise Bulls next week.