Wriddhiman Saha, reprieved by Renshaw on nine, was unbeaten on 10 at stumps alongside Ravindra Jadeja (16 not out).
"It's an unbelievable feeling to be pretty evenly poised after day two," Lyon said.
"We probably left a few runs out there but to have them 6-240 odd, I am quite happy.
"Coming over here everyone wrote us off and to be in this position in the last Test with pressure slightly on India is fantastic."
Pacemen Pat Cummins and Josh Hazlewood huffed, puffed and bowled exceptionally well but only claimed a wicket each.
"Josh and Cummins in the first session, I can say it's the toughest session I've faced in Test cricket," India's top-scorer KL Rahul said of the testing examination that ended when he fell victim to a bouncer from Cummins.
India resumed at 0-0 with every intention of grinding the visitors into submission with a mammoth first-innings total, as was their plan in Ranchi.
The ploy looked to be working well when Cheteshwar Pujara, who spent over 11 hours at the crease during a game-changing knock of 202 in the third Test, brought up his half-century in 132 balls.
Pujara guided India to 2-157 before becoming the first of Lyon's four victims, falling in the opening over after tea when he offered Peter Handscomb a simple catch at short leg.
Lyon then removed Karun Nair, stand-in skipper Ajinkya Rahane and Ravichandran Ashwin.
And the Australian tweaker delighted on a pitch that allowed him to trouble batsmen with bounce as much as spin.
"It was closer to a home wicket, where the bounce is my biggest weapon," Lyon said.
"I went back to how I bowl (at home).
"As the day progressed there was more variation with bounce and spin."
Lyon also varied his speed a lot more after a debrief with skipper Steve Smith at tea.
"It was a bit of a tactic," Lyon said.
"If you looked at the way the Indians have been playing me, especially Ajinkya (Rahane), my plan was to come over the wicket and try and get him not to sweep me so my stock ball would be more effective."
Cummins and Hazlewood each had two overs with the second new ball. The former found the edge of Saha's bat, however Renshaw failed to complete the dismissal.
- AAP
