Only once in their opening 11 games this season have the SPL champions hit the net more than twice, when they crushed Inverness 4-2 last month.
It was the same story again at the weekend when, despite having 23 shots on Dundee's goal, they had to settle for a 2-0 victory.
Although Lennon was delighted to see the Hoops move up to third spot in the table, he wants them to sharpen up in front of goal.
And, with the Scottish Communities League Cup a trophy Lennon wants to win for the first time as a manager, tomorrow's third round tie against Raith Rovers would be as good a occasion as any for his men to hit the conversion target set by him.
"I think someone is going to be on the tail- end of one pretty soon," said Lennon with an ominous warning for every other club.
"We are just waiting on it all to click together.
"There were times when we tried to walk the ball in against Dundee, or took one pass too many, and were not as clinical as we could have been.
"But we created loads of chances, and that pleased me more than anything."
Gary Hooper and Victor Wanyama were the only men to take advantage and beat an inspired Rab Douglas, who had earlier saved Scott Brown's penalty.
Lennon admired the display of his former Hoops team-mate, but remains confident that, some time very soon, another keeper is going to be picking the ball out of his net on multiple occasions.
He said: "Once we get the combinations right in our attacking play, I think the goals will come.
"Lassad Nouioui made his first start on Saturday and Gary Hooper came back from injury.
"Hopefully we will have Miku for tomorrow night. He had a bit of fatigue after midweek and should be okay.
"Then Tony Watt is on call if we need him."
Lennon wants to increase competition across the board and is delighted Joe Ledley and Beram Kayal resumed training yesterday after groin and ankle injuries respectively.
"The Raith game may be too early, but I'll discuss that with the medical team," said Lennon.
He added: "Paddy McCourt is fit again, and Georgios Samaras will possibly be able to start training again after the weekend."
