Lyon sealed top spot in the Europa League standings while Roma survived a red-card scare to reach the last 16 on a chaotic final league-phase night.
Lyon's lack of recent action has left him stalled on 562 wickets, one shy of Glenn McGrath's tally in the list of most prolific Australian test wicket-takers.
'To be able to take over or equal Glenn, or however you want to put it, it's pretty humbling to be honest with you, and it's something that I'll look back at the end of my career, or even tonight, and sit back and try and have a moment.'
AS Roma took a big step towards qualifying for the Europa League last 16 with a 2-0 win over VfB Stuttgart on Thursday.
During England's run-chase of 435 runs, Lyon had taken three crucial wickets in the second innings and a total of five throughout the game to help his side gain an upper hand.
Ashwin said bluntly that Lyon is "lucky" to be in a system where a player can vent without fear of fallout.
Chasing a world record 435 runs to win, England were reduced to 207 for six at stumps on Day 4 of the third Test, still 228 runs short of victory
Australia's Lyon angry at being dropped for second Ashes Test
Steve Smith said the decision to drop Nathan Lyonwas taken to strengthen the pace-bowling department.
Captain Pat Cummins and spinner Nathan Lyon have returned to the Australia XI for the third Ashes Test against England in Adelaide.
Lyon thump Maccabi Tel Aviv to go top, Forest keep on winning
Spinner Todd Murphy has been called into the Australia squad in place of the injured Nathan Lyon for this week's fourth Ashes Test, while captain Pat Cummins will skip the rest of the series as his back issue is managed.
Images from Day 2 of the 3rd Ashes Test in Adelaide on Thursday
'We know we're behind the game again, in the situation we currently stand.'
Australia head coach and selector Andrew McDonald has confirmed Usman Khawaja will play in the fifth Ashes Test against England at the Sydney Cricket Ground amid media speculation it could be his last international.
With the Ashes urn in their hands, Australia decided to rule Cummins out of the two remaining Tests.
t Pat Cummins' side firmly on top of the WTC standings, with a perfect record after six matches in the current cycle.
'They're those little moments as a squad that I think have got us across the line to four wins this series.'
Regular captain Pat Cummins was named in the Australia squad on Wednesday for the third Ashes Test against England, a strong indication that the inspirational fast bowler will see his first action of the series in Adelaide next week.
England opener Zak Crawley said Australia had shown why they were favourites coming into the Ashes after a tough day four at Adelaide Oval left the tourists staring down the barrel of a series defeat on Saturday.
Starc reached his second fifty of the series in 73 balls, striking eight fours, before England finally struck back. Archer ended Lyon's resistance, trapping him plumb in front for 9, and Australia were soon bowled out for 371 in 91.2 overs.
'I think it's a huge credit to (head coach) Andrew McDonald, the coaching staff and the medical staff that we feel like we've got a big squad that we can draw on.'
Triumphant Australia will bid farewell to Usman Khawaja as England look to recover another few scraps of pride when the Ashes series comes to a conclusion with the fifth Test in Sydney from Sunday.
'We could play a couple of all-rounders. Could play a spinner. Could play no spinner. We'll figure it out.'
Australia may opt to continue with a four-prong pace attack at Adelaide and even add another part-time seamer in all-rounder Beau Webster, who could replace batter Josh Inglis in the lower middle order.
Khawaja pulled no punches, taking aim at former players and sections of the media over what he described as blatant double standards
IMAGES from Day 5 of the 3rd Ashes Test in Adelaide on Sunday.
The Ashes could be decided within days at an Adelaide Oval furnace where England's hopes of wresting back the urn will fire anew or flame out entirely against a strengthened Australia.
Kevin Pietersen criticises England after their Ashes loss in Adelaide
Steve Smith returns to action in the Boxing Day Test against England as Australia opted to include four fast bowlers in their 12-man squad.
''South Africa have got some world class batters and obviously they've got some unbelievable bowlers there as well so it's going to be a good challenge and obviously it's a one-off Test match.'
An Ashes tour that began with high hopes of taking home the urn has been reduced to a desperate effort to salvage some last vestiges of dignity for England.
The overwhelmingly bowler-friendly Melbourne pitch on which 20 wickets fell on Day 1 of the Boxing Day Test has prompted Kevin Pietersen and Dinesh Kartik to point out the selective criticism of Indian tracks when spinners get wickets in a heap.
Aston Villa secured a 2-1 victory at Basel on Thursday, with goals from Evann Guessand and Youri Tielemans keeping their Europa League campaign on a strong footing.
It was a wild ride while it lasted but the 'Bazball' revolution that enlivened English cricket for three years collapsed in 11 days on Australian soil in an Ashes defeat as harrowing as any in the modern era.
The 3rd Test match in Kingston, Jamaica, will mark Australia's first day-night Test away from home and if they opt for a pace-heavy attack, Scott Boland could come into the side.
England need to alter their approach if they hope to claw their way back after their disastrous start to the Ashes series and avoid another drubbing, former Australia paceman Mitchell Johnson said.
'Dad played the biggest role in my cricket, coached me all the way through and sort of let me go as I got into my older teenage years, but (he) would always shoot a message (like) 'put the reverse sweep away'.'
'It's a moment I'll never forget, having my family there.'
Starc also pointed out that the wicket did not assist pacers that much with the new ball and expressed concerns over Nathan Lyon's injury on the final day of the Test and the setback to Hazlewood.