Misbah misread a googly from part-timer Steven Smith and was caught at mid-on after scoring a solid 69 and adding an invaluable 93 runs for the fifth wicket with Asad Shafiq.
At the break, Shafiq was batting on 56 and Sarfraz Ahmed was unbeaten on 27 as Pakistan added 109 runs in the morning session after resuming at 219-4.
Misbah, under pressure to score after managing just 67 in the 2-0 Test defeat in Sri Lanka two months ago, hit two boundaries and two sixes during his 255-minute stay at the pitch.
Lyon was unlucky not to have dismissed Shafiq off the first ball of day's second over when Alex Doolan failed to catch a bat-pad push at forward short-leg. Shafiq by then had not added to his overnight score of nine.
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Misbah, who was 34 overnight, reached his first half-century in nine innings with a push for single and then launched an attack, hitting Lyon for a six over long-on.
He also hit Smith for a six but played one shot too many, holing out much to the delight of the Australians.
Shafiq has so far hit four boundaries during his 107-ball knock.
Johnson was the pick of bowlers with 3-33.
Younis Khan made a sparkling 106 on the first day after Pakistan won the toss and batted.