Sri Lankan off spinner Ramesh Mendis dismissed David Warner (25) lbw and had Marnus Labuschagne (13) caught by Asitha Fernando in Australia's innings to finish the day on 2-35.
Khawaja was batting on 47 with Travis Head on 6 at stumps.
Earlier, Lyon returned bowling figures of 5-90 and leg spinner Mitchell Swepson had 3-55 to help Australia bowl Sri Lanka out to a modest score.
Niroshan Dickwella top scored for Sri Lanka with 58, his 21st test half-century. He added 42 runs for the sixth wicket with Angelo Mathews (39) after Sri Lanka lost five wickets for 97 runs, and 54 runs for the seventh wicket with Mendis (22).
Sri Lanka opted to bat first after winning the toss and resumed its innings after tea at 191-6.
Lyon trapped Mendis lbw with just two runs added to to the teatime score to end his partnership with Dickwella.
Dickwella edged Lyon to wicketkeeper Alex Carey and had Lasith Embuldeniya (6) as his fifth wicket.
Australia's second spinner Mitchell Swepson took two consecutive wickets in the 37th over with identical deliveries. The leg spinner got the first delivery of the over drifting toward right-handed Dananjaya de Silva's leg stump and the bouncing ball took a fine outside edge for a catch to wicketkeeper Carey.
De Silva made 14.
Dinesh Chandimal was dismissed first ball when the ball turned, bounced and rebounded to Warner at second slip from wicketkeeper Carey's glove.
Captain Karunaratne and Pathum Nissanka opened the batting for Sri Lanka and added 38 runs for the first wicket.
Fast bowler Pat Cummins forced an edge off Nissanka (23) with a rising delivery to wicketkeeper Carey and four runs later Starc had No. 3 batsman Kusal Mendis (3) driving far from his body for an edge to Carey.
The home team named three spin bowlers for the match, including leg spinner Jeffrey Vandersay for his test debut. The 32-year-old has taken 25 wickets in 19 one-day internationals and seven wickets in 14 Twenty20 internationals for Sri Lanka.
The series is being played for the Warne-Muralitharan Trophy, named after the two top bowlers in test history with 1,508 test wickets combined. This is the first series for the trophy after Australian great Shane Warne died in March from a heart attack while vacationing in Thailand.
A brief remembrance was held for Warne before the match.
The Australian leg spinner — who took 708 test wickets behind Sri Lanka's Muttiah Muralitharan's 800 — took his 500th test wicket at this ground in 2004 and helped rebuild the ground after it was destroyed by the Asian tsunami later that year.