The Hoops skipper was handed an additional two matches on top of his automatic one-game suspension after being sent off in the Group H clash against Barcelona earlier in the month for flicking a leg out at Neymar after having fouled the Brazilian.
Brown missed the 2-1 win over Ajax at Parkhead on Tuesday night and will also sit out the return match in Amsterdam next month and the visit of AC Milan, unless his appeal is successful.
Lennon questioned Brown's sending off after the Barca game and the player later admitted he had "made a mistake" but felt the red card was "harsh".
Ahead of Sunday's Scottish Premiership clash with Partick Thistle at Firhill, the Hoops boss said:
"It (appeal) is going to be next week at some stage.
"I don't know if I am going over but there will be representation from the club and Scott as well.
"We would like him there - if he is going to go - to put his point across.
"He has a good disciplinary record and I think that should stand him in good stead as well."
Lennon returned to another potential disciplinary matter by addressing fully for the first time comments made towards him by Hibernian forward Rowan Vine on Twitter following Celtic's 1-1 draw at Easter Road last Saturday.
Lennon had complained about Hibernian's tackling in the match and Vine had taken exception to the Northern Irishman singling him out for a challenge on Hoops debutant Darnell Fisher. Lennon described it as "rugby-esque".
Vine made reference in his Twitter postings to an incident in a Newcastle versus Leicester game in 1998 when Alan Shearer kicked Lennon, then a City midfielder, in the head.
The Englishman wrote: "Read Sir Neil Lennon's comments regarding tackles in y'days game and said my tackle was 'rugby-esque'. I mean I know he likes the snus. But has he been smoking something else. I hardly touched the boy and there were no 'reckless' tackles in the game.
"Might get me mate Alan Shearer to send him another size 9 Umbro Speciali in the dish if he don't pipe down."
Lennon replied on his own Twitter account, writing: "Did I read that right?"
Vine later apologised to Lennon and Hibernian boss Pat Fenlon said he dealt with the issue in-house after speaking to the player.
However, the Scottish Football Association confirmed to Press Association Sport that the matter is being looked at.
Lennon said: "I am assuming the authorities will look at it, rather than myself. There is nothing I can do about it.
"I don't run the game and I don't make the laws up. I think there is a line you can't cross when it comes to saying anything in public, either personal or against a club so I will leave that to the powers that be.
"We have had discussions about it (use of social media) yes, with the players regarding themselves and their wives as well."
In the absence of traditional city rivals Rangers from the top flight, Lennon is looking forward to an alternative Glasgow derby against Maryhill men Partick, who have yet to win a home league game this season after returning to the top flight.
He said: "It is a derby and I haven't had one of them for a while so I am looking forward to it.
"I could literally walk to the stadium from the house - but I'm not going to, obviously.
"I am sure it will be a full house and a cracking atmosphere.
"Thistle have been excellent. I watched them against Hibs and they were very unfortunate not to get at least a point and they had a brilliant result (against Inverness) last week.
"Their style of football is very pleasing on the eye."
- Sports & Recreation
- Neil Lennon
- Partick Thistle
- Alan Shearer