The Celtic coach has been discussing his meeting with the former Bhoys boss.
The pair met up to watch Celtic's Development Squad face Manchester City and Deila admits he enjoyed exchanging wisdom with the man who held the hot seat at Parkhead before him.
Although they only spoke for five minutes, the Norwegian says everything Lennon told him was relatable. And the Bhoys boss also revealed what Lennon said to him about a potential domestic treble.
Deila told reporters: "We were talking about our situations, Bolton and Celtic. Of course he knows my role and how this club is, so it was good. It was a nice conversation.
"We only talked for five minutes but he knows what Celtic is all about. He said a lot of things that I can recognise and understand. Hopefully we will meet again and have a longer chat."
On the club's Treble bid, meanwhile, Deila said of Lennon: "Yes. He is a Celtic fan so he wants the best for us."
The Hoops face Inverness Caledonian Thistle at Hampden Park on Sunday afternoon in the Scottish Cup semi-finals.
They will be buoyed by their most recent 4-1 Scottish Premiership win over Kilmarnock but may retain memories of the drab 1-1 draw v Inverness last weekend.
Lennon never achieved a treble with Celtic, with the club not having won one since 2001. The chance, then, is there for Deila to make history - and now he knows for sure he has his predecessor's backing.