Lennon enjoyed the feeling of being Clydesdale Bank Premier League champions for the first time as a manager on Saturday following a highly eventful two years in the post.
"I am so proud of him and so thrilled and delighted for him," Lawwell told Celtic TV's Huddle Online programme. "He has come through a very, very turbulent two years. The pressures of being Celtic manager alone are immense."
Lennon has been sent bullets in the post, suffered a pitchside attack and two men are awaiting sentence for sending him parcel bombs.
Lawwell was delighted with the nature of Celtic's title-winning 6-0 victory over Kilmarnock on Saturday, and the connection between the manager and about 13,000 fans who filled three stands at Rugby Park.
"It's very, very intense and having to deal with other matters, he has done it admirably well. He is a fighter, he is a man of great, strong character and I'm absolutely thrilled for him."
An emotional Lennon sparked speculation over his future in the immediate aftermath of the game when he remarked that he would consider his future as usual in the summer with reference to the off-field issues but he appears certain to continue in his role.
"He is a young man, he loves this football club, he loves the supporters and that is something that is very, very important to Neil," Lawwell said.
"It's very important that we have a manager who does love the supporters and the club. He is a guy that I'm sure will be successful here and hopefully for a very long time."
Lennon admitted he felt vindicated after the title triumph. "People were maybe not sure I justified being Celtic manager because I was so inexperienced. But they are going to have to take me seriously now," he told Celtic TV.
Source: PA
Source: PA