The Russian side – who come to Parkhead on Wednesday for the final Group G game which could open the door to the Last 16 for the Hoops – crashed 4-2 at home on Friday to Zenit St Petersburg.
The defeat comes on top of a humiliating 5-1 loss to city rivals Dynamo – a result that cost manager Unai Emery his job.
Fomer boss Valery Karpin stepped back down from the boardroom to try and steady the Spartak ship.
But the heavy defeat to Zenit confirmed how big that job will be.
Nevertheless, Lennon is cautioning against anyone believing Spartak – who are expected to have fit-again Aiden McGeady in their starting XI – will be there for the taking for a tie in which Celtic must better the result Benfica record in Barcelona on the same night to go through to the Last 16.
Lennon said: "We watched Spartak on Friday when they lost to Zenit, and they're having their own problems domestically.
"I don't know what frame of mind they will come to Glasgow in – but I do know they are a dangerous team.
"They attack very, very well and were unfortunate at times against Zenit.
"They had a spell of dominance when they looked very, very dangerous going forward. So we will have to be mindful of that."
Spartak are determined to avenge the 3-2 home defeat they suffered against Celtic on Match Day Two which effectively scuppered their chances of joining Barcelona in qualifying from the group.
Lennon is not being fooled by their current domestic form, which has seen them tumble down the league, and said: "They went in as half time against Zenit 2-1 down, but didn't deserve to be behind.
"Going forward, they are a real handful. We're going to have to try to win the game and we will wait all night if we have to for the goal. But we must emphasise the importance of keeping a clean sheet, and I think our players will rise to the occasion."
Lennon is also confident the Celtic support will again turn out to play a huge part in adding to the occasion on Wednesday.
Only around 15,000 attended Saturday's Cup tie against Arbroath. But the manager refuses to use the empty stands as any excuse for the shock result.
"I don't think the atmosphere had anything to do with it on Saturday," he insisted. "The fans were great.
"We'll now just have to go Arbroath and win the tie there – but I'll definitely go with a different team."