Bairstow was given out 15 minutes before the interval which led to tensions rising on and off the field with Australian players abused in the Long Room as they left the field.
While players from the respective teams went into their own dressing rooms they came face-to-face again in the lunch queue with both sides sharing a dining area at Lord's.
"There were a few Australian guys and a few English guys in the lunchroom and I hobbled up on my crutches and stood in the middle of it and tried to calm things down a little bit." Lyon, who by then had been sidelined with a calf injury, told the Willow Talk Cricket Podcast which is co-hosted by former Australia wicketkeeper Brad Haddin. "Jonny had a few words here or there. That's all part of it, I'm all for it."
Lyon was also in no doubt about the dismissal. "I was in the change room and I just erupted. I was like 'how good. Suck eggs. That's out every day'," he said.
The abuse of the Australian players in the Long Room, which appeared to centre on Usman Khawaja and led to security being called, has resulted in three MCC members being provisionally suspended while the club investigates.
Lyon said that "everyone was gobsmacked" by how the situation escalated following the dismissal and also talked through a first-hand account of a spectator from inside the pavilion approaching him outside in tears and apologising for the abuse the Australian players had received.
"I actually had an older lady come up to me in tears, an English lady in tears from the main members' area, and she said 'I've got to go home. I just want to apologise to you Australian cricketers for the way everyone has reacted inside the Lord's", Lyon said.
"I just told her don't worry about it, we're all okay, we're not worried about getting sledged. But it hit home for me that Ashes cricket can affect so many people in different ways and just the actions of people can hit so many different people as well. It was a nice moment but an awkward moment with the lady in genuine tears about it all."
Meanwhile, Lyon admitted he knew his Ashes tour was over the moment he suffered the injury on the second day although he was only officially ruled out after the match finished. "[Ben] Duckett played the pull shot, got a top edge and I went to take off and I just heard this little gun shot and just felt it go straight away. I knew straight away my series was done there and then," he said.
Lyon still hobbled out to bat in Australia's second innings, adding 15 runs for the last wicket with Mitchell Starc, after he persuaded the medical team he was able to do it when they had initially told him it wasn't an option. "I knew I was out for the next 10-12 weeks. So I took a couple of tablets, got strapped from my knee down, couldn't move my foot at all and hobbled out, stood in the Long Room and waited to bat."
Despite what could be a three-month timeline for his recovery, Lyon is confident he will be able to get a substantial amount of Sheffield Shield cricket before Australia's next Test series against Pakistan which starts in mid-December.
"The positive thing about all this is I've got a lot of time," he said. "The next Test match that Australia will [play] at home is mid-December against Pakistan. I've got plenty of time…to make sure we do the rehab and we do it properly so it's not a reoccurring thing. I'll definitely get some Shield in. I'm not going to say I'll be right for game one. Ideally I'd like to play that but I'm not going to push it."
There are six rounds of Sheffield Shield before the Test summer begins, which is also when the tournament breaks for the BBL, with New South Wales' opening match on October 4.
Lyon admitted he had found it tough to watch the Ashes while sidelined back in Australia and only caught glimpses of the Headingley match.
"I've had a lot of emotion around my first-ever injury and the timing of it in what was meant to be a pretty big milestone for myself," he said. "So they boys are talking that I've only played 99.5 games in a row. Pretty shattered but the guys are in decent position. I find it hard to watch Test cricket now - I've figured that out - so we'll see how we go."
Andrew McGlashan is a deputy editor at ESPNcricinfo