Mr Lyle, the founder of the popular supporter-led YouTube channel, said he was subjected to abuse in Tottenham High Road after leaving the ground on Sunday.
Video footage from the scene showed Mr Lyle and two other men surrounded by police, dressed in riot gear, who appeared to be guiding him through the crowd.
One fan appears to shout: “Come this way, you black c***.”
In a tweet posted later that evening, My Lyle said: “I had people calling me a black c***. It was a small minority but it's not on. This is 2017.”
Speaking during a video posted on the Arsenal Fan TV channel, he added: “I was racially abused today. I have not had that at a football ground for years. There is no other football ground in the Premier League that I go to, that I get what I got today.
“Basically, if the police weren't around who knows what could have happened. It was disgraceful. Tottenham are building this brilliant ground and it's looking amazing, I'm not going to hate on it, but if they don't do something about security for away fans there is no point in building that ground.”
Mr Lyle claimed Tottenham club officials had instructed him that Arsenal Fan TV could not carry out its usual post-match interviews in an area of Park Lane where Spurs fans had been shut off from.
The fan who filmed the footage and cannot be heard speaking during the video told the Standard he was not aware of anything racist being said.
The Standard has approached Met Police to ask if they are investigating the video.
A spokesman said on Sunday that six people were arrested for a variety of offences outside the ground including public order and possession of a flare.
"Officers dealt with some disorder outside the ground prior to the game and the matter was swiftly dealt with. An appropriate and proportionate policing plane was in place," the spokesman added.
A spokesman for Tottenham Hotspur said: "We are currently looking into this matter further with the Metropolitan Police.
"We strongly condemn the use of racist and offensive language and we will take the strongest possible course of action against any supporter identified of using such language."