At 157 for two, and with the dependable Cheteshwar Pujara and stand-in skipper Ajinkya Rahane looking set in the middle, India appeared to have the upper hand before Lyon (4-67) intervened after tea.
In the first over of the final session, Lyon sent back Pujara for 57 and went on to dismiss Karun Nair, Rahane and Ravichandran Ashwin to deflate the hosts.
Ravindra Jadeja clobbered a couple of sixes and was batting on 16 at the close, while Wriddhiman Saha was on 10, having survived two reviews and a dropped catch.
India are still 52 runs behind Australia's first innings total of 300 in the decider of the four-test series which is level at 1-1.
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"It's an unbelievable feeling, to be pretty evenly poised after day two," Lyon told reporters.
"I know we probably left a few runs out there but to have India six down for 240-odd after a pretty a good day on the field -- (I am) quite happy to be honest."
Pat Cummins and new ball colleague Josh Hazlewood were aggressive in the morning session on a pitch which offered wholesome bounce to the pacemen.
Hazlewood was rewarded for constantly attacking the line outside the off-stump when Murali Vijay edged him to Matthew Wade to depart for 11.
Fellow opener Lokesh Rahul was hit on the index finger of his right hand by a Hazlewood delivery but the right-hander recovered to score 60 and give India a strong start.
The 24-year-old left well, drove elegantly and slog-swept Steve O'Keefe for a six en route to his fifth half-century of the series.
The second-wicket partnership was worth 87 runs and was looking ominous until Rahul went for a wild hook, with the bouncer hitting the toe end of his bat before finding David Warner at mid off.
Rahane found himself in the line of fire and the otherwise dependable batsman made things difficult for himself by trying to pull and hook his way out of trouble.
Pujara, who batted for more than 11 hours in the drawn third test in Ranchi for his 202, played with characteristic calmness at the other end and brought up his fifty with a boundary off Lyon.
The off-spinner claimed a major breakthrough when he ended Pujara's nearly three-and-half hour vigil by getting him caught at short leg.
Leading the side in absence of injured regular skipper Virat Kohli, Rahane fell to Lyon for 46 with Australia skipper Steve Smith taking a sharp catch at slip.
Ashwin made 30 before he was trapped leg-before by Lyon.
"All of us got starts but we could not convert," Rahul said of his top and middle order colleagues.
"We're happy. (At the) end of the day, (nearly) 250 runs for six wickets was not really the worst day for us."
(Editing by Toby Davis)
