The Russian giants are already consigned to the bottom of Group G but will have a say in who joins Barcelona in the knockout stages of the Champions League.
If Lennon's men better Benfica's result in the Nou Camp, then the Hoops will qualify for the next stage of the competition.
Karpin took over the helm after Spaniard Unai Emery was dismissed following a 5-1 thrashing by city rivals Dynamo last week.
But the Parkhead boss, whose side won 3-2 in the Luzhniki Stadium in October, is worried that Karpin's presence will change the attitude of his players.
He said: "We know a lot about Spartak, obviously we have played them already.
"We have analysed their matches, home and away and we will study them again before we start preparing for the game.
"They have a new coach in, Karpin, although he has been there (at the club) a long time.
"Whether that changes the attitude of the players....it might be a good thing or bad thing, I don't know."
The visit of Spartak is just one of eight games Celtic will play in December, but Lennon has played down the possible effects of such a gruelling schedule.
"That is just the reality of it," said Lennon. "It is nothing new for us. This season has been game after game after game. The challenges are there for the players.
"Christmas is always a heavy schedule but we have got the extra SPL game against Dundee United at home. It is a course of games to get our teeth into and we are really looking forward to it."