Lustig came up against Deila's Stromsgodset team during his time with Rosenborg before moving to Glasgow in January 2012, and was not surprised to see them winning the title last year.
The defender was reunited with Deila today as the Norwegian and assistant John Collins welcomed the players back for pre-season training and Lustig admits he is excited about the future at Celtic Park.
The 27-year-old said: "He likes to play on the ground, attacking football, a lot of combinations, and when we faced them at (Stromsgodset's) home, I found it really hard to beat them. I never won against them when they were at home. They played great football and I heard he was really good with the young lads.
"He is probably the most exciting manager in Scandinavia right now so I'm really happy to work with him."
Lustig believes 38-year-old Deila's ability to improve young players, such as Celtic's January signing from Stromsgodset, Stefan Johansen, will be invaluable when they begin another Champions League campaign against KR Reykjavik in mid-July.
"Stromsgodset is quite a small team in Norway, they don't have the money of the big clubs," he said. "So that was a real achievement.
"They won the league last year, but the year before that they were at the top as well, so it wasn't a shock that they won the league. They have played really good football for some years now.
"He is really good with the young lads. Stefan is just one guy who has done really well, some other guys went to France as well.
"Maybe Celtic don't have as much money to buy players who are really good right now, so if he is going to develop the young lads, that will help us."
Despite his enthusiasm for Deila's reign, Lustig was sorry to see the departure of the man who brought him to Parkhead, Neil Lennon.
"I thought that he was going to stay here for at least one more year, but you never know in football, things happen so quickly," the defender said. "I don't know everything that happened there but I'm just grateful that I played under him."
Lustig is looking to hit the ground running this season after returning from a five-month lay-off in the closing stages of last term.
"I had a problem with my hip, but I was in really good form and probably playing the best football of my career," he said. "I knew had to have the operation but it was bad timing.
"It's tough when you feel you can't finish a game and you are always thinking about how you are feeling. You try to do your best but you know it's going to hurt.
"Right now I feel really good so it's going to be really important for me to stay fit now, especially as we are going into the qualification so quick. I'm going to work really hard to stay to fit."
Lustig showed his commitment to Celtic by signing a new three-year contract days after Lennon's exit.
"I really love to play for this club so it was never a hard choice," he said.
"I can play in Europe every year, the fans are amazing, and if I want to change clubs I will need to pick a smaller club. Maybe more money, but it's going to be a smaller club. I'm not that good to choose a bigger club than Celtic.
"And my family really love it here as well so it was never a hard choice."