The Lions are due to play the Japanese in Edinburgh on Saturday June 26 before flying to South Africa for a three-Test series against the world champions.
The French Top 14 final is scheduled to take place on the previous evening, which means Russell would be unavailable the Japan game if his Racing side were to make it through to the decider.
The Scotland stand-off is considered to be a leading contender for the Lions tour and the Japan game could potentially offer him the chance to put a marker down for selection for the Test team.
Racing are currently third in the Top 14 standings. The play-off semi-finals are scheduled for the weekend of June 19-20.
The Murrayfield fixture is fast turning into a major headache for Lions head coach Warren Gatland. As well as clashing with the French final, the game will also be played on the same day as the English Premiership final, potentially robbing the Lions of a clutch of leading players.
Gatland would like to work with his Lions squad for two weeks leading up to the Japan match but this is being resisted by PRL, the umbrella group which represents England’s leading clubs.
It could mean that Gatland will be denied access to all English-based players - even those not involved in the Premiership play-offs - before leaving for South Africa.
The problem looks particularly acute at stand-off, where Northampton’s Dan Biggar and Saracens’ Owen Farrell are likely to be hamstrung by the PRL stance.
If Russell is also ruled out, it could leave Johnny Sexton as the senior available No 10 to face Japan. The Leinster outside-half, who turns 36 in July, has been the Lions’ Test No 10 in each of the last two tours.
Back-up at ten could come from Glasgow Warriors’ Adam Hastings.
Gatland, meanwhile, has called for “common sense to prevail” when Lions chiefs meet PRL this week in the hope of thrashing out an agreement.
Speaking on Tuesday, Gatland said: “We understand about the Premiership final and players involved in that, but we hope to be together for a couple of weeks of preparation leading into the warm-up game against Japan.
“If some players are not available for that preparation time, there are some tough calls to make. What we are asking is can they be released a little bit earlier, when they’ve finished their club campaign?”
However, Exeter Chiefs rugby director Rob Baxter has described the Lions’ stance as “a little bit disingenuous”.
“The Lions have known the Premiership schedule for a long time now – I think about a year – so they have known exactly what the scenario was, they’ve known there is no way of cutting that season short,” said Baxter.
“Everyone has known when the Premiership season is going to finish, so for the Lions to now turn around and say that this is a scenario is a little bit disingenuous, I think, because they have known our fixture list for a long time.”