Postecoglou was appointed as his replacement in the summer and Lennon has been hugely impressed with the work of the former Australia head coach, revealing the pair have chatted on numerous occasions.
Lennon, who is now in charge of Cypriot side Omonia Nicosia, has watched his former side undergo a complete rebuild and he pinpointed the one Postecoglou signing he would have liked to have had at his disposal last season.
Lennon told PLZ: "Ange's been a breath of fresh air. I think his style of football is great to watch.
"I think he's a genuinely a really good guy. I've spoken to him on a lot of occasions.
"He's rebuilt the squad, which needed doing, everybody knew that.
"But I think some of the players he's brought in have been fantastic.
"I really like Kyogo Furuhashi and I wish I'd had Joe Hart last season!
"Ange is on the cusp now of winning the title which would be a remarkable achievement.
"You never say it's over until it's over, but you've got six points and a really good goal difference.
"Obviously losing the semi-final is a sore one but over the piece they've been so consistent since October.
"Psychologically the win against Rangers in February was a huge shot in the arm for the club and Ange himself.
"They've been imperious domestically up until Sunday."