After Mitchell Starc's 54 helped Australia to 371 on the second morning, England started well in their reply to move to 0-37 with Duckett flying.
But three wickets in the space of 15 balls have left the tourists reeling, with Joe Root also surviving a close caught behind call just before the break.
After Pat Cummins caught the edge of Zak Crawley to have him caught behind for nine, it was Lyon who took over at Adelaide Oval.
Lyon first ensured Ollie Pope's miserable tour would continue, with England's No.3 playing a poor shot when he turned a ball straight to Josh Inglis at mid wicket.
Pope is now struggling to hold his spot in England's side, with the tourists staring down the barrel of an irrecoverable 3-0 series deficit if they are beaten in Adelaide.Â
The next dismissal was all Lyon.
Coming around the wicket to the left-hander Duckett, he drifted the ball into the England opener and then turned it away to take the top of off stump.
Duckett looked stunned, offering a bewildered response similar to that of Mike Gatting after Shane Warne's ball of the century at Old Trafford in 1993.
Lyon's double strike took him to 564 Test wickets, past Glenn McGrath and into second on the all-time Australian list and sixth worldwide.
It also marked something of a statement, after he was left out of Australia's attack at the Gabba with the pink ball in use.
Root was then lucky not to go in the next over on 0 with England 3-42, when Australia reviewed a caught behind appeal.
Replays showed the ball did take the England star's inside edge, but third-umpire Chris Gaffaney decided the ball had touched grass on entering Alex Carey's gloves.
It marked the second big DRS drama of the match, with Carey surviving a caught-behind review on 72 on his way to 106 on day one for Australia.
The operators of snicko have since confirmed a human error denied England the wicket and a spike should have lined up when the ball passed Carey's bat.
Earlier on Thursday, Starc's second straight half-century had helped Australia reach a competitive score, with the hosts able to add 50 for the final two wickets.
Starc crunched five boundaries through the offside in the opening few overs of the day, before Scott Boland also finished 14no.
Australia's ability to make their tale wag has been crucial so far in this Ashes, after Starc's 72 at the Gabba proved crucial.
Starc and Lyon (9) both ultimately fell to Jofra Archer on Thursday, who was England's clear stand out bowler with 5-53 after a tough few Tests.
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