The Hoops are looking to extend their unbeaten Scottish Premiership league run to 20 games against the Buddies and are odds-on to retain their title this season.
However, Celtic's last three matches have been won by a single goal and the Parkhead boss noticed a flatness in the second half of their match at home to Partick Thistle on Wednesday, where a Joe Ledley drive made the difference.
The Northern Irishman is looking for one big effort from his players before they fly out to Turkey for a winter break - albeit they are scheduled to play two games in the Antalya Cup, a tournament which also involves Galatasaray, Trabzonspor and Dutch champions Ajax, whom the Hoops faced in their ill-fated Champions League group.
"There was definitely a tiredness creeping into the team in the second half against Partick," said Lennon.
"I just want us to play with a little more zest.
"We have had a heavy schedule of games recently but we have had an extra day (over St Mirren) to recover from the Thistle game.
"So hopefully we will see a wee bit more energy in the team, that is what I am looking for."
The champions are 11 points clear of Motherwell with a game in hand over the Steelmen as they continue their march towards the title.
However, Lennon does not believe the ninth-placed Saints, whose form has been indifferent this season, will be the expected pushover.
The former Celtic skipper said: "They like to play football but they will play with a bit of intensity, so I expect it to be a harum scarum type of game.
"They beat Dundee United 4-1 and I know they lost to Kilmarnock on Thursday, but by all accounts they deserved something out of the game. And St Mirren have give us some really tough games at their place.
"The season before last we won 2-0 but they caused us all sorts of problems and we had to rely on Fraser Forster to make some really good saves.
"Obviously, they beat us in the semi-final of the League Cup last year, so it is going to be as tough a game as we have had in quite a while."
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- Partick Thistle