Sri Lanka were looking confident after Kusal Mendis and Kusal Perera's 108-run stand, but their departure after lunch saw the hosts in some trouble.
Skipper Angelo Mathews, with his unbeaten 49, then ensured Sri Lanka stay in the hunt after electing to bat first on a bright sunny day. He has Dhanajaya de Silva (9 not out) for company.
Starc (3-44), who marked the day with his 100th Test wicket, denied first-match centurion Mendis his second consecutive ton after getting the in-form batsman caught behind for 86.
Mathews came to the crease with a positive mindset as he made the reverse-sweep his stock shot against Lyon. His 55-ball stay was laced with two fours and three sixes.
Earlier Mendis' 137-ball stay was laced with 10 fours and two sixes as he entertained a lively home crowd at the Galle International Stadium.