The former Hibernian striker returned to Tynecastle for the first time since completing his £1million move from Wolves on Saturday to net his opening Celtic goal against old foes Hearts.
Griffiths struck 28 goals during his final season at Easter Road last year as he claimed both the Clydesdale Bank and Scottish Football Writers' player of the year awards.
But Lennon believes the 23-year-old Scotland cap is ready to click up another notch.
"He's settled in fine," said the Parkhead manager. "Getting the goal will have given him a huge psychological lift.
"He has been brought here to score goals and there is an expectation on him now. He's playing for the biggest club he's had in his career now but he's adapted to it very well and the players around him have made the transition easier for him.
"It will be a weight off his shoulders to get that goal so early in his time here. He's a goalscorer and if you look at his finish, it was a typical Leigh Griffiths finish.
"He strikes the ball with so little back-lift but with a lot of power and unerring accuracy. We like his movement and his intelligence and I think there is more to come from him."
Celtic travel to Aberdeen on Tuesday night but Lennon insists the Bhoys do not have vengeance on their mind following their shock Scottish Cup defeat by the Dons earlier this month.
"Revenge is a bit too strong a word really," said the Northern Irishman. "It's just a case of us maintaining our focus away from home."
The Reds' win at Celtic Park sparked claims that Derek McInnes' men were closing in on the Hoops in terms of the strength of their squads.
But while Lennon's unbeaten side notched up their 23rd league win from 26 games as they beat the Jambos 2-0, Aberdeen slipped to a 3-1 defeat against Partick Thistle to fall 24 points behind the runaway leaders.
And Lennon says that only proves just how impressive his side's feat has been.
"Those things can happen," he said. "It speaks more about what we have done in the league this season then any other team.
"On any given day you can get beat. We had a bad day a couple of weeks ago and it cost us our place in the cup.
"But our league form has been fantastic. We have got 12 games to go and we have got a real drive for the players to see us through now."
Lennon is determined to see his side write their names into the history books by ending the campaign with a blemish-free run in.
Keeper Fraser Forster has already set a new Scottish clean-sheet record for league matches after extending his shut-out tally to 1,215 minutes. He now trails former Manchester United number one Edwin van der Sar's Britsh count by just 96 minutes.
But Lennon says players must remain vigilant if they want to continue their special season.
He said: "Fraser was very proud after the match at Tynecastle but he wants to maintain his form. He's got the British record to go for now.
"But it's difficult to talk about breaking records. Our focus is on winning the next game. Both the clean-sheet and undefeated record could go at any time, so we will have to be at the top of our game tomorrow night."