When it comes to mixing it with Europe's elite, as they proved in their Group G opener at home to Benfica during the week when they shared the spoils, raising their game for such occasions most certainly isn't a problem for Celtic.
The adrenaline rush Champions League football automatically injects into the Parkhead players, and the supporters for that matter, means lifting his men for those matches is never likely to prove difficult for Lennon.
When it comes to taking on Benfica, Spartak Moscow and Barcelona the only worry – perhaps challenge is a better way of putting it – for the boss is to make sure his tactics are spot on and his players carry them out on a stage where they must be at their very best simply to hold their own.
Domestically, however, that isn't the case. If anything, the biggest challenge for the defending champions is making sure they lift themselves sufficiently for matches to the stage where their superiority over the opposition becomes evident.
So far this season, that hasn't always been the case as seven points being dropped in their opening five league games suggest. On Saturday, however, his players managed to get the goals at the right time and record a 2-0 victory over Dundee.
It was more efficient than excellent from Celtic. There were times when the pace of the game was far too slow and not enough was happening in the final third. That is when you need individual talent to be the difference and it most certainly was at the weekend.
Gary Hooper was the man who stepped up to the plate by netting an outstanding opening goal just when it appeared as though former Hoops keeper Rab Douglas – who had already made a brilliant save to deny Scott Brown from the penalty spot – was going to have one of those days.
And after the break, it was a terrific low strike from Victor Wanyama that doubled his side's advantage and made sure Celtic returned to winning ways in the league. Although disappointed at the amount of chances his team passed up, Lennon was much happier with the overall display.
He said: "It was a good performance with a clean sheet and three points and two quality goals so I'm pleased with the way we went about our business.
"Maybe we are a little flat after European games and I can understand that. However, we still need to get out there and win the game.
"I've told the players I want us to now be more consistent in the league and it was good to get the win and get moving up the table.
"Obviously it is difficult when you have European matches to contend with but we have to keep producing every time we go out there.
"It was great to see Gary Hooper get on the scoresheet and it was an excellent goal. He worked it very well with Scott Brown and the second goal was a special strike from Victor Wanyama. He is capable of that. So, over the piece, I was pretty pleased with our efforts."
If anything, the only disappointment for Lennon was seeing his players pass up as many goalscoring opportunities as they did.
"You also have to give big Rab Douglas credit for the way he performed," said Lennon of his former team-mate who was in top form between the sticks for Dundee. "But yes, I'd like to see us be more clinical.
"The amount of chances we are passing up is a concern. We are working the ball well up to the final third and we need to just make sure our delivery is better and that we try and do things a little quicker."
If the challenge for Lennon is to make sure his players are as up for every domestic match as they are for big European nights, then he might need to emphasise the importance of not taking their eye off the ball tomorrow when they host Raith Rovers in the League Cup.
Lennon is determined to lift as much silverware as possible this season and is likely to make a couple of changes to his starting line-up with Joe Ledley and Beram Kayal returning.
He added: "The games are coming thick and fast and fortunately we've got a couple of players back and we will maybe make a change or two anyway. However, we still expect a strong performance."