Die Roten go into the game having won nine games on the bounce, which is a streak currently shared with Barca.
Lahm says that, although the Champions League holders have already qualified for the knockout stages, the incentive to make history will spur them on in Moscow.
"This is a very important game for us," Lahm told Kicker. "We want to have the record on our own and keep it going for as long as possible."
The Bavarians coach Pep Guardiola stressed that it will be a tough game for his side, particularly after the effort it took to beat rivals Borussia Dortmund 3-0 at the weekend.
"There is no doubt that this will be a difficult game for us," the Spaniard said.
"We beat Dortmund, which was very important for the club and the players. Although we have already qualified from the group stages we still obviously want to win this match."
Bayern winger Arjen Robben, 29, added: "We take a huge amount of confidence from the Dortmund game, but we know this will be tough."
MasterCard is excited to present episode three of the Priceless Memories Uefa Champions League video series. See what Manchester United legend Andrew Cole had to say!