Bristol looked to have turned the game around last weekend after a 51-26 victory over Gloucester – just their third win of the season.
Lyon, who are 12th in the Top 14, like Bristol, have won just three games this season and both sensed a potential rare win in a frantic opening period.
Bristol had the perfect start when Gabriel Ibitoye’s pass to the bin sent over Richard Lane in the corner.
However, the French responded with two quick touchdowns. Scrum-half Martin Page-Relo played a key role in both of these actions – first his accurate pass provided a simple finish for Ethan Dumortier and then a moment of individual brilliance with a break and long pass to Marvin Okuya doubled Lyon’s lead.
The first half continued as Benhard centre Janse van Rensburg’s pass was picked up by Samoa representative Steven Luatua, who was able to stretch his long arm to the try line. Next on the scoring list was hooker Harry Thacker, who attempted a goal from the back of a rolling maul.
Although the high tempo and pace did not slow down as the half approached, the accuracy of both sides diminished after covering over 200 metres in the first half.
The second half continued in a similar fashion and the pace picked up after the break in what was a truly exciting encounter.
Bristol travel to Bordeaux Begles next Saturday, while Lyon take on Bulls, who beat Saracens 27-16.
Callum Sheedy kicked a drop goal in the 85th minute that denied Lyon an incredible Investec Champions Cup victory.
Bristol appeared to be heading for victory with a bonus point after Gabriel Oghre’s fifth try and taking a 33:10 lead.
However, two tries from Thaakir Abrahams along with a touchdown from Semi Radradra set up a top-level finish.
Alfred Parisien’s solo try seemed to have won the game with three minutes to go before Sheedy struck.
South African Abrahams showed good speed to finish the try from nothing after an optimistic offload landed in the winger’s arms.
The 2020 Challenge Cup winners lost control of the match when winger Kalaveti Ravouvou was sent to the bin with 17 minutes to go after a dangerous finish.
With a numerical advantage and confidence after the goal, Lyon threw themselves into the attack through former Bears centre Radradra, who spotted a gap in the ruck and went over.
Abrahams again showed sharp acceleration to complete another score before Parisien cut in with what looked like the winning try.
However, Bristol tore up the pitch with the clock in the red and set up Sheedy, who converted the ball in front of the posts.
Bristol salvage a great opening period
The match at Ashton Gate was a duel between two teams struggling for form in their respective leagues.
Bristol Bears – Lyon 36:34
Bristol: Malins; Ibitoye, Vakatawa, Janse van Rensburg, Lane; Sheedy, Randall; Woolmore, Thacker, Sinckler, Dun, Batley, Luatua, Harding, Bradbury.
Lyon: Abrahams; Dumortier, Parisien, Radradra, Ioane; Smith, Page-Relo; Taofifenua, Charcosset, Tafili, Kpoku, Geraci, Okuya, Pacheco, Guillard.