The Russian side crashed to a 4-2 defeat 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 coach Unai Emery his job.
Fomer boss Valery Karpin stepped back down from the boardroom to try and steady the Spartak ship but the defeat to Zenit shows how big that job will be.
However, Lennon remains cautious about the threat Spartak - who could have fit-again Aiden McGeady in their side - will pose at Parkhead.
"We watched Spartak on Friday when they lost to Zenit, and they're having their own problems domestically," Lennon said.
"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."
The Glasgow giants sit third in Group G on the same points as Benefica and need to better the Portuguese side's result against Barcelona if they are to progress to the next stage for the first time since 2008.
Spartak will finish bottom of the group no matter the result in Glasgow but will be determined to avenge the 3-2 home defeat they suffered against the Hoops which effectively ruined their chances of qualifying from the group.
Lennon, whose side could only manage a 1-1 draw with Second Division Arbroath in the Scottish Cup at the weekend, said Celtic will have to show patience and discipline if they are to get the win they need.
"I'm not sure if the majority of our fans expect us to go through and that may work in favour of our players," he said.
"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.
"As a team, they're a bit more flamboyant than Benfica who are more pragmatic and maybe better defensively.
"There's a bit more flair and pace in this Spartak team although they do throw caution to the wind sometimes and leave themselves open.
"I think we have to be careful attacking-wise because Russian teams historically are excellent on the counter attack. In Emmanuel Emenike they've got a goalscorer.
"At the back, though, I don't think it's their strongest area.
"We have to make sure our set-up is right and play with the intensity we can, but make sure we're mindful of our discipline in defence as well."
Celtic should have almost a full squad to pick from although winger James Forrest is ruled out through injury.
Source: AFP
Source: AFP