The Hoops' boss believes Tuesday's opposition are a significant step up from their previous games, but has faith his team can give a good account of themselves in Russia
The Celtic Park outfit recorded solid victories over HJK Helsinki and Helsingborgs to qualify for the group stages of Europe's elite club competition, but the Northern Irish coach conceded that their next opposition would be a step-up in class.
Lennon saw his side grab a draw with Benfica in the Hoops' opening group tie at Parkhead and is keen to build on that performance to improve their away record in Europe.
"Those questions aren’t asked as much now, but away from home in the Champions League is the toughest game you can get in football," Lennon told reporters.
"We are aware our record is not so great – but records are there to be improved upon. We played well in Helsinki and Helsingborgs and it's given us a lot to be encouraged about.
"We know it's going to be very tough. Spartak Moscow are an excellent side with an excellent coach. Going forward, they have players who are very quick, strong and skillful. They are very rigid in the way they play.
"But we are coming into the game in good form. Our away form in Europe has been pretty good recently, but this is a real step-up for us in terms of class and competition. "
Lennon admitted that the pressure is off his side after merely making it to the group stage, but called for a run of good performances to build expectation levels back up among fans after beating Motherwell 2-0 in a table-topping SPL clash on Saturday.
"We have touched on this before," he added. "All the pressure was in the qualification and the games against Helsinki and Helsingborgs.
"Now the expectation is less than it would have been but I suppose if you are playing well - and we got off to a decent start in the group - then the expectation levels start to build again.
"Our performance at the weekend was probably our best of the season so if we can build on that going into this game, who knows where it can take us. "
The Celtic boss also played down suggestions the artificial surface in the Luzhniki Stadium could have a detrimental effect on his side's game, and pointed towards previous experience of playing on plastic pitches that will help them adjust.
"We will have a look at the pitch tonight but I don´t think it will be a problem because we played in Helsinki and that experience will benefit us going into the game tomorrow," explained Lennon.
"We will have to stop their forward players getting in between the lines and hurting us. We will have to defend well and counterattack as best we can."