McCleary, who made Reading's opening goal and scored the second in their 3-0 quarter-final replay win, was targeted by a Bradford supporter when he later took a corner and the winger reported the incident to match officials shortly before half-time.
"I heard about that and when we find out who it was we will take action," Lawn told Press Association Sport.
"I understand the police are prosecuting so we can't do anything at this stage, but if that person is found guilty we will take action.
"There is no place for that in the game, it is unacceptable.
"I would think we're looking at a lifetime ban if he's found guilty but that decision can only be made after consultation with the club's board."
Reading confirmed in a short statement after the game that the incident had been reported to the police, while Reading manager Steve Clarke said McCleary had been "upset by something".
A brief statement from Thames Valley Police read: " A 36-year-old man from Bradford was arrested on suspicion of indecent/racial chanting at a designated football match (Football Offences Act 1991) and he has been bailed until 16th April."
Later in the game a bare-chested Reading fan ran on to the pitch and was led away by match stewards after performing a series of cartwheels
Supt Jim Weems, who led the policing operation at the Madejski Stadium, said: "Thames Valley Police made a small number of arrests at last night's football match at the Madejski Stadium in Reading and will investigate all reports of offences thoroughly.
"Overall it was a successful policing operation in partnership with Reading Football Club, with minimal disorder
The vast majority of fans watched the game in a positive and pleasant atmosphere."
Thames Valley Police refused to comment further on individual cases, but confirmed three other men from Bradford had been arrested, plus a 20-year-old man from Wokingham.
Source : PA