The 29-year-old made the most of a lively track at Dharamsala, which is hosting its first Test, to return a rich haul of 4-67 in the final session of play.
Fast bowlers Josh Hazlewood (1-40) and Pat Cummins (1-59) also bowled their hearts out during frugal spells to restrict the hosts to 248-6 at stumps.
India trail by 52runs with four wickets in hand after Australia made 300 in their first knock, largely thanks to a fine 111 from captain Steve Smith.
At stumps Wriddhiman Saha was batting on 10 with Ravindra Jadeja on 16.
With the series in the balance at 1-1, the game's two top-ranked sides have been locked in a battle of attrition, with neither willing to give an inch.
"I reckon it is an unbelievable feeling to be pretty evenly poised after day two," Lyon said after the day's play.
"I know we probably left a few runs out there, but to have India 240-6 odd after a pretty good day in the field, I am quite happy to be honest.
"Coming over here, everyone wrote us off and to be in this position in the last Test at 1-1 and the pressure slightly on India is fantastic."
The Indian batsmen were guilty of squandering good starts in a match they must win to regain the Border-Gavaskar trophy.
But Lokesh Rahul (60) and Cheteshwar Pujara (57) batted patiently to put on 87 for the second wicket, the best partnership so far for the hosts.
"It's by far the best wicket we have played on, there's something in it for the spinners and the fast bowlers as well. The ball kept swinging the whole day," said Rahul.
"If you spend some time in the middle it's really good to bat on. All of us got starts but we couldn't convert.
"But we are happy at the end of the day with 250-odd runs for six wickets. It wasn't really the worst day for us."
Ajinkya Rahane, standing in for injured skipper Virat Kohli, also looked set for a big score but ended up gifting a catch to Smith off Lyon for 46 off 104 balls.
Ravichandran Ashwin (30) was adjudged lbw off Lyon. The all-rounder opted for a review but the ball tracker showed the stumps would have been hit.
Lyon, who had conceded 163 runs while taking just one wicket in the previous drawn Test at Ranchi, remained wicketless in the first two sessions.
But the bowler, whose experience as a curator gave him a sharp understanding of pitches, brought Australia back into the game in the final session through some classic old-fashioned spin.
Lyon's first victim was Pujara, who wascoming into the match on the back of an epic innings of 202 at Ranchi.
Pujara tried to defend but the ball ripped back in to hit the glove and then lob up to short leg, where Peter Handscomb pouched an easy catch.
Pujara's 57took his run tally past 400 in the series, behind only Smith who has 482 runs from seven innings.
The Indians would have been in further trouble but for Matthew Renshaw who dropped two catches, much to the frustration of the toiling bowlers.
But the Aussies have the chance to run through India's tail with the second new ball on Monday morning and grab the crucial first-innings advantage.
Day two also saw words being exchanged with long stares on a couple of occasions. But mostly the players remained within the bounds of good behaviour in what has otherwise been a fractious series.
Australia, who triumphed at home against India in 2014-15, need just a draw to retain the trophy.