The Hoops had to fight their way through two qualifying rounds and were then unfancied when drawn alongside the Russian club, Benfica and Barcelona.
However, with seven points from five games, including a famous 2-1 home win over the Catalan giants, the Scottish champions will go through to the last 16 if they get a better result against Spartak, who are consigned to the bottom of the table, than Benfica get in the Nou Camp.
The former Celtic skipper, who became boss of the Parkhead club in 2010, said: "It would be my best achievement as a manager here.
"It would be great for everyone associated with the club and it would give the players something to look forward to and get their teeth into in the new year.
"No one gave us a prayer coming into the competition.
"There were people saying we wouldn't get a point and people saying we wouldn't get into the Europa League but we felt that we had a decent chance and that's what we have given ourselves.
"However, regardless of the outcome, we will have European football (in the new year) and that was one of the targets going into the group.
"Which competition it is in remains to be seen but we would all love to be in the Champions League, obviously."
Celtic's task may have become more difficult with the news that Barcelona are set to leave out Javier Mascherano, Jordi Alba, Xavi Hernandez, Cesc Fabregas, Andres Iniesta and Pedro Rodriguez for the visit of the Portuguese club.
However, Lennon said: "I am not concerned with what other teams are doing in the competition.
"I am concerned with my own team and how they play tomorrow evening, and regardless of whether Barcelona leave six players out, the six players who come in will be quality.
"What I want is for us to win the game and that would mean Benfica would have to win in Barcelona."
The Northern Irishman knows that in such a night of tension the score from the Barca game will filter through to his players, but he said: "I don't think we can stop that getting through from the crowd but the players will be focused regardless of the result elsewhere.
"I want them to be concentrated. It is a difficult enough task as it is.
"The remit is to win the game and 10 points would be a fantastic total.
"If that gets us through then great, if it doesn't then it is still a tremendous effort."
Spartak's former Celtic winger Aiden McGeady admitted after arriving in Glasgow today that the Russian club, with just three points from five games, have been in turmoil in recent months.
Manager Unai Emery was sacked following the recent 5-1 derby defeat to Dynamo Moscow and replaced by caretaker coach Valery Karpin, who saw his side lose 4-2 at home in the Russian League to Zenit St Petersburg on Friday night.
Lennon, though, warned against the assumption that Spartak will simply take on the role of bit-part players in what could be a momentous night for Celtic.
"Karpin may make changes and they may come and play with freedom given that they don't have any pressure coming into this game, other than their own pride and their supporters' pride, and that can be a dangerous ingredient for us," he said.
"They are a very good team going forward, they have goals in them, a lot of flair and flamboyance in the way they play, so we will have to defend well at times although we feel there are goals in our team as well."
Lennon is happy with the cover he has for midfielder Victor Wanyama, who is suspended after picking up another booking against Benfica in Lisbon to take him over the points limit.
He said: "He has had a fantastic season for us and has been very consistent.
"He picked up an unfortunate booking, we felt, against Benfica and he will be a loss.
"But that is subsidised by the fact that Beram Kayal is more or less fit now and playing very well and Joe Ledley and Scott are in contention as well."
Lennon played down reports that striker Miku is set to cut short his loan spell from Spanish side Getafe.
He said: "We had a wee chat yesterday. He is happy here.
"He knows he can do better but he wants to stay and be a success and I am very happy with that."