Lyon, his bowling consistency questioned by his captain Steve Smith, produced an inspired two wickets in three balls to put Pakistan on the slide.
He coaxed Younis Khan to push forward and be caught by Peter Handscomb centimetres off the ground at short leg for 24 and then dismissed skipper Misbah-ul-Haq to an injudicious sweep for a duck.
Misbah swept outside his off-stump to Nic Maddinson placed at short fine leg for the premeditated shot.
Lyon struck again just before tea when he had in-form Azad Shafiq snapped up by Handscomb at silly mid-off for 16.
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Pakistan go into the final session at 91 for five with first innings double-centurion Azhar Ali on 34 and Sarfraz Ahmed on one and still trailing by 90 runs. Off-spinner Lyon had figures of three for 21 off 10 overs.
Mitchell Starc followed up his big-hitting 84 in Australia's innings, with the wicket of Babar Azam on the first ball after lunch. Azam was trapped leg before wicket for three after Sami Aslam was bowled by Josh Hazlewood off a bottom edge for two in the second over of the innings.
He called a halt to a massive first innings at 624 for eight -- remaining unbeaten on 165 off 246 balls -- to give his fast bowlers a crack at the Pakistan openers just before the interval.
The decision to declare was accelerated by Starc's big-hitting knock of 84 off 91 balls. Starc clubbed seven sixes, the most in an innings in a Melbourne Test, and was severe on Yasir Shah, belting the leg-spinner for five sixes.
He was given a reprieve on 51 when he skied spinner Azhar Ali to long-off where Sohail Khan fumbled the two-handed chance. He took to Azhar hoicking him for successive sixes and then blasted another six off Yasir before he was finally out caught by Shafiq at backward square leg.
Starc put on 154 runs for the seventh wicket with Smith off 172 balls and upon Lyon's dismissal, caught and bowled by Yasir for 12, Smith said that was enough and raced from the ground.
It was the skipper's 17th Test century and fourth for the year and he will finish 2016 with 1,079 runs at 71.93.
Australia lead the three-Test series 1-0 after beating Pakistan by 39 runs in the Gabba Test.