The 38-year-old Norwegian emerged as a surprise candidate for the post following Lennon’s departure two weeks ago.
High-profile names such as Henrik Larsson, Owen Coyle and Steve Clarke were all linked to the job while Republic of Ireland assistant manager Roy Keane asked not to be considered after initial talks with the Scottish champions.
Speaking at the media conference at Celtic Park yesterday where Deila, who guided Stromsgodset to their first title in 43 years last season, was confirmed as the new Hoops boss, Lawwell said: “Neil mentioned in an interview today that when (former assistant) Johan (Mjallby) left we had a chat about Ronny in terms of if he could play a role here.
“When Neil decided to go and the process started two weeks ago, Ronny was at the top of the list to go and have a chat to. Things came to a head only in the last day.
“We were in Norway yesterday and this morning he (Deila) got to talk about his own terms and conditions.
“There were no job offers (to other candidates).
“We spoke to a lot of people at different stages and got to different levels but no offer was made to anyone else.”
For his part, Deila has rejected comparisons with top German boss Jurgen Klopp to insist he is his own man.
Deila, who guided Stromsgodset to the title last season and the Norwegian Cup in 2010, has been compared to the highly-successful Borussia Dortmund manager, whose football philosophy has earned him many admirers.
Deila confirmed that former Celtic and Scotland midfielder John Collins was one of several candidates to be his number two, while Lawwell admitted he was in talks with former Hearts and Sunderland keeper Craig Gordon.
When asked if he was the Norwegian version of Klopp, the new Celtic boss replied: “No, I am Ronny Deila. But I like Jurgen Klopp. He is a modern leader, very close to the players, and I think that is important. You have to get the players to feel safe and they also have to feel loved, and Jurgen Klopp is fantastic at doing that.
“He also has good offensive play which gives energy to a stadium, and when you have a stadium like Celtic Park, you need energy in the stands and on the pitch. But I don’t think too much about it. I am me and I have to be me. I hope somebody one day will say ‘he is like Ronny Deila’.”
Klopp himself congratulated the Norwegian. “A great club with great fans gets a great manager. I’m very happy for Ronny Deila and wish him every success at Celtic.”
Lawwell described Deila as a “progressive, intelligent and modern” manager with “a fantastic track record in winning and developing a team”. “He fits perfectly with where we are as a club,” Lawwell added.
The Norwegian’s first competitive game as Celtic boss will be a Champions League qualifier next month, the first of three the Hoops have to negotiate to reach the group stages of the competition.