ByKolles had skipped the Sebring FIA World Endurance Championship round at the start of the year in order to switch from Nissan's turbocharged V6 unit to the more proven naturally-aspirated Gibson V8 also used by the Rebellion Racing and DragonSpeed LMP1 teams.
The ENSO CLM P1/01 made its debut with the Gibson engine at Spa, where it enjoyed a trouble-free run until Dillmann was put in the barriers by the Oreca LMP2 of Jordan King.
In the run-up to Le Mans, Dillmann explained that the cold conditions in Belgium had prevented ByKolles from getting a full understanding of its new-configuration car, and the test day at La Sarthe - held in hot conditions - exposed problems it had not discovered prior.
Dillmann and his teammates in the #4 car, Oliver Webb and Paolo Ruberti, managed to complete 163 laps in the race itself before retiring with a terminal gear selection problem at around 4am.
"We were a bit late with the project, with the new engine," Dillmann told Motorsport.com after the race. "We were a bit behind.
"We missed mileage to find these issues before Le Mans, the car was finished way too late, just before Spa. It should have been finished earlier, that was the plan. We were not ready."
#4 ByKolles Racing Team Enso CLM P1/01: Oliver Webb, Tom Dillmann, Paolo Ruberti
Dillmann believes that, with one of the SMP BR Engineering BR1s crashing out and both Rebellion R-13s enduring fraught races, a top-five was on offer for a clean run.
"Even though we were not really quick, if we had a smooth race, we could have finished fifth," he said. "We would have finished in front of the second Rebellion which was  laps down.
"That was the aim, but it didn’t happen. We were not reliable enough."
DragonSpeed electrical dramas strike again
Besides ByKolles, the only other LMP1 non-finishers at Le Mans were the #17 SMP car, after a night-time crash for Egor Orudzhev, and the Gibson-powered customer DragonSpeed BR1.
Ben Hanley, Renger van der Zande and Henrik Hedman shared the Gulf-coloured #10 machine for its swansong LMP1 outing, but repeated electrical gremlins ended their charge at around 3am.
"We had a lot of problems all week, especially with the electronics," van der Zande told Motorsport.com. "We worked until Saturday to try and solve the issues, but every time a different problem came up.
"It’s a massive disappointment because we invested a lot of time, money and energy in getting this car to the start. The positive thing is that the team wants to return to Le Mans [next year], but with a bulletproof car, probably an LMP2."
DragonSpeed is switching its focus to its fledgling IndyCar programme for the 2020 campaign, and will resume its partial schedule in the series at Road America this weekend with Hanley.
Additional reporting by Filip Cleeren
#10 Dragonspeed BR Engineering BR1: Henrik Hedman, Ben Hanley, Renger Van der Zande