"I've always said I am not about personal milestones or personal achievements, it's about winning Test matches and Test series for Australia," said Lyon.
"I haven't really had the time to sit back and think about it," added the 31-year-old who got to the mark in 88 matches -- 18 more than Lillee, who played the last of his 70 Tests in 1984.
The often outspoken Lyon, who prior to Australia's 4-0 2017/18 home series win in the last Ashes campaign said he hoped the team could "end the careers" of several England players, has rarely given the impression of lacking confidence.
But he insisted he felt awkward with the company he was now keeping.
"I really struggle to see myself up with the likes of Warne, McGrath, Lillee, it doesn't sit well with me," Lyon said.
"In my eyes those guys are true legends of the game and I'm just some bloke trying to bowl off breaks and trying to make Australian fans proud of the Australian cricket team."
At stumps, in a match where Wednesday's first day was washed out without a ball bowled, Australia were 30-1 -- 228 runs behind.
There was no question that Australia, 1-0 up in the five-match series after their 251-run win in last week's first Test at Edgbaston -- a match where Lyon took 6-49 in the second innings - had enjoyed the better of the day's play.
But they did drop several catches and saw England recover from a woeful 138-6 despite recalled fast bowler Josh Hazlewood (3-58) and new-ball partner Pat Cummins (3-61) also taking three wickets apiece.
"I don't think we have had the best day, if I am being brutally honest," said Lyon.
"Josh Hazlewood was absolutely exceptional and the spell from Pat Cummins after tea really set the tone for us.
"For our standards I don't think we were good enough for long periods of time.
"In saying that it's still a good day for Australia. We haven't played catch today, we can get better and that's exciting, but we were still able to bowl England out for 258 on a day one wicket," he added.
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