The Celtic manager believes that the midfielder has been unfairly vilified in the wake of his red card in Tuesday's defeat to Barcelona with too much made of his petulant flick.
Brown will be back in the team today and Lennon is also optimistic that Uefa will not see any justification in extending the ban to further than one game when they convene on October 17. As such, he has decided against investigating a possible appeal and will now count his losses for this month's Champions League game against Ajax.
"They take each individual incident on its own merit and I'd like to think a one-game ban would suffice," he said.
"Scott is fine. He is obviously disappointed, but he has my backing, he has the players' backing and he has the backing of the national team manager as well. He will play today.
"There has been a huge improvement in him. His form was patchy to say the least but we have got him fit and injury-free which is great and you can see what he brings to the team. We are talking about an isolated incident from the last three or four years and the hysteria following it is over the top because it has come under the microscope in such a big game.
"I still feel it is not a red card. I still feel he should not have put himself in that position but when I look back at the game and some of the other challenges in the game he was really hard done by.
"I had a chat with him after the game but you move on. We'll miss him for the Ajax game but we'll have him for the remaining three games. At the minute there is no extra sanction and that's the way it should be."
Derk Boerrigter, Tom Rogic and Joe Ledley will miss today's meeting with Motherwell, with Georgios Samaras a significant doubt, although James Forrest has trained and midfielder Nir Biton is expected to be fit despite suffering from a bug.
And Lennon has no doubt that his side will be able to lift themselves for the visit of Stuart McCall's side.
"I think sometimes when you play the best, the cream, and you come away thinking you've competed, run them close and you're not uncomfortable in that environment, it gives you a huge lift," he explained.
"That's the benchmark for the players and sometimes you get inspired by games like that. It gives you extra motivation to try to reach that level of performance and I'm hoping that will be the case for this game.
"I don't think I'll need to lift the boys too much because the majority of them can be really pleased with the contribution."