Abdullah Shafique and Azhar Ali struck half-centuries in opening session to take Pakistan to 159 for 1 and also ensured that Australia had to walk back wicketless.
Lyon dismissed Shafique early in the second session for 81.
Cummins struck with the new ball to remove Azhar Ali as Pakistan went to Tea at 227 for 3.
Rizwan was able to manage just one as Pakistan slipped to 256 for 5 in the final session.
Pakistan lost 7 for 20 to fold for 268 and conceded a lead of 123 with Babar making a half-century.
Cummins bagged five wickets while Starc got four as Australia edged ahead at stumps.