Now the Celtic manager wants to see that gap increase over the festive period with the distraction of the Champions League put on the back burner for a couple of months.
A comfortable 2-0 win over St Mirren, thanks to goals from Victor Wanyama and Gary Hooper, allowed the Parkhead club to open up a four-point advantage at the top of the table with the possibility of increasing that to seven points by winning their game in hand.
It was also Celtic's first home league victory since late October after losing to Kilmarnock, drawing with St Johnstone and then losing again to Inverness, results that brought criticism of Lennon and his players despite their achievements in Europe.
Demanding an improvement in domestic results in the wake of their successful attempts to progress into the last 16 of the Champions League, it appears as though the manager's message has come across loud and clear with three consecutive victories.
Lennon was pleased to see his players go about their business in such an efficient manner and provide the home support with something to shout about, but he says it must continue over the next couple of months.
"It was a very pleasing performance," said Lennon. "I thought we played the game at a good tempo, we enjoyed plenty of possession and we were patient in our build-up play and created a number of chances to win the game.
"You are always a little nervous at 1-0 so it was nice to get the second goal and I don't think it was any more than we deserved.
"The lads know we've not performed as well as we would have liked in home league matches recently and it was nice to put that right and get the three points in the bag. That's us four points clear at the top of the table which is nice because we need to focus completely on the domestic scene right now.
"I said after we managed to qualify for the last 16 of the Champions League that I wanted us to completely focus on our league form. There are always a lot of games at this stage of the season so hopefully we can keep things going now.
"That's us four points clear with a game in hand and that's decent."
It was another match in which Lennon continued to go with a changed formation of 3-5-2 and it is a system that allows the Parkhead club to throw numbers forward.
It was also another 90 minutes which highlighted just how much of an eye for a player Lennon has.
Adam Matthews enjoyed a fine game wide on the right, Waymana strolled through the match in the middle of the park as did Beram Kayal.
Efe Ambrose was even doing a bit of showboating as he found himself at the centre of many of his side's attacking moves as a result of St Mirren defending at the edge of their box.
As much as there has been one or two who haven't blown everyone away, Lennon's success rate in the transfer market will go a long way to attracting the attention of English Premier League chairmen who would have also taken notice of his side's Champions League heroics.
Certainly, two of his best signings, Wanyama and Hooper, were the men to get on the scoresheet with Wanyama forcing the ball home from close range after his initial header from a Charlie Mulgrew corner was blocked. Hooper was in the right place at the right time to convert with just seven minutes remaining.
What happens now in Europe for Celtic remains to be seen. The last 16 draw takes place on Thursday and, with a bit of luck in avoiding a number of the favourites to lift the Champions League, they might just have a chance to make history by qualifying for the quarter-finals.
But those games are a couple of months away and in between times the players have got to make sure they string together a run of results that allows their advantage at the top of the table to increase significantly, even if it means grinding out results against teams who offer little in return.
As for St Mirren, well, they contributed absolutely nothing to the game. Danny Lennon is someone who likes to preach on how the game should be played and the importance of trying to play with style, but there was nothing fashionable about having just about every player behind the ball for virtually 90 minutes.
Their tactics would get football stopped. The game plan was to try and suffocate Celtic but when they went behind you would have thought they might be slightly more adventurous. You would have been wrong. It's no wonder attendances are decreasing across the SPL.
It made it a far from entertaining match but, when facing a team with such negative tactics, the priority for Celtic is to simply win the game. They achieved their target.
They must continue to do that to allow the Champions League to then become the focus again next year.