Several Argentine networks showed footage of the incident in which Lombardi was seen to follow the man out of a car park and down the street to challenge him to a fight.
Lombardi, who had a cut near his left eye, squared up to the man like a boxer sparring with an opponent and lashed out, but a policeman prevented any of his punches from making contact.
The exchange, which went on for at least five minutes before other policemen arrived, took place in a busy street in central Buenos Aires and onlookers could be heard in the background egging on the pair.
Argentine media identified the other man as Fabio Garcia, who was an assistant to Leonardo Madelon, Lombardi's predecessor at San Lorenzo.
Lombardi told reporters that Garcia had attacked him in the car park although that was denied by Garcia. Both men were taken to a police station and later released, media reports said.
The quick-talking Lombardi, famous for speaking his mind, has criticised Madelon's work at San Lorenzo since taking over in April, especially regarding the fitness of the players.
Lombardi has coached 16 professional clubs in Argentine and has earned a reputation as a rescue worker.
He famously saved Racing Club from relegation three years ago and, although he failed to produce a repeat performance with Quilmes last season, he left them well placed for promotion when he departed for San Lorenzo in April.
Known as 'The Saw' during his playing days as a hard-tackling midfielder, the stocky 50-year-old has been involved in numerous verbal slanging matches with players and coaches.
San Lorenzo, regarded as one of the big five Buenos Aires clubs, are 17th in the relegation standings which would force them into a two-leg play off against team from the second division.
The club has been beset by incidents of violence in and around their ground which is adjacent to a notorious shanty town.
Captain Jonathan Bottinelli was hit by a hard-core fan during an argument after training in October and a junior player was stabbed in the stomach by young supporter in February.
In a more recent incident, fans tried to storm the match officials' changing room angry that referee Diego Abal allowed visiting Colon's controversial equaliser in a 1-1 draw, a decision he admitted the following day had been a mistake.
Relegation in Argentina is decided over three seasons.
