This week the Hoops boss said that the Scottish Football Association must be consistent with their rulings for manager bans following a few incidents of that nature this season.
Lennon received a four-match touchline ban for clashing with Rangers number 2 Ally McCoist in early March – his second sanction of the season – and said he will be very interested to see what happens to Brown after he clashed with Motherwell chairman John Boyle recently.
But Brown said he is not bothered by Lennon’s comments and plans to stay out of any potential war.
“I am aware of what's been said but I won't get involved because I won't be talking about another club or another manager, certainly not in a detrimental way at least as I always praise the opposition manager if they win,” Brown told SunSport.
"I never criticise them so I don't think it's appropriate to say anything.
"It's up to him what he says but I'm better to say nothing.
"I have been asked to respond to the SFA by the 10th of May on the incident at Motherwell.
"I've written them a letter and from what I understand an appearance at their disciplinary hearing on that date is optional as the response I have given should do."