Martin O'Neill's former right-hand man has been impressed with a set of performances that included the club's first away win in the Champions League group stages against Spartak Moscow and that famous Parkhead victory over Barcelona.
Now he is refusing to count out the chances of a third remarkable result.
Robertson said: "Getting to the last 16 was an incredible achievement because, in my opinion, the Barcelona team are the greatest that has ever been.
"So, for Celtic to overcome them – and nearly get something in Barcelona too – was fantastic. A fabulous achievement.
"When the draw was made and they got Spartak Moscow, Benfica and Barcelona, a lot of people might have thought they wouldn't have had a hope. But to come through it is incredible.
"Their escapades in Europe have really brought the club to the forefront again. People must have looked at that Barcelona result and thought: 'Well that Celtic must be a decent team'.
"You don't beat Barcelona unless you are a very decent team. Can a miracle happen in Turin? Realistically, everybody will tell you no. Not many teams come back from there with a result.
"But until the tie is over, there has to be hope. Why can't we go over there and get a result?"
Robertson was O'Neill's assistant when the Northern Irishman lured compatriot Lennon north of the border in a £5.75m switch from Leicester in December 2000.
It was during that time that he first saw the leadership qualities in the midfielder that have allowed him to become one of the most highly-rated young bosses in the game.
He said: "Neil has always been an intelligent lad and as a foot-baller, he was a very, very intelligent player too.
"He spoke well and knew the game, so it was no surprise to me that he would go on and become a manager.
"He came in at a difficult time when he had no experience of being a manager but has really grown into that role."
Robertson, however, believes Lennon will prove himself to be a different kind of coach to O'Neill.
"I've not seen Neil work as a manager but I'm sure some of the principles of the game he will take from Martin, just as he would have taken from Dario Gradi and Gordon Strachan.
"Ask Martin O'Neill if he was another clone of Brian Clough and he will tell you that you can only be yourself.
"It's impossible to try and copy someone else so just be yourself, and Neil is doing wonderfully well doing just that."
Robbo was at Hampden to help conduct the draw for the William Hill Scottish Cup semi-finals.
Celtic were paired with Dundee United and will meet at Hampden on either April 13 or 14.