The West Indies seem destined to follow-on, trailing Australia by 460 runs. Darren Bravo was 13 not out at stumps and Carlos Brathwaite on 3.
Openers Kraigg Brathwaite and Rajendra Chandrika provided a decent start, putting on 35 runs for the first wicket before the innings quickly fell apart.
Offspinner Lyon (2-18) made the breakthrough shortly after tea when Brathwaite was caught by Joe Burns at forward short-leg for 17.
Pattinson (2-36) then removed Chandrika lbw for 25 and Marlon Samuels, also lbw, for a duck to make it 50-3.
Bravo and Jermaine Blackwood briefly steadied the ship before Lyon ended their partnership by removing Blackwood (28) caught and bowled.
Siddle (2-19) had Denesh Ramdin (0) caught by Burns with an athletic, diving effort at square leg, and knocked back the off stump of Jason Holder (0) with the next ball, as the West Indies lost three wickets for one run.
Blackwood looked to be out while on 18 when Burns took a diving catch off Siddle, but after a long deliberation by the on-field and TV umpire, it was decided the ball did not carry.
Australia began the day at 345-3, and overnight batsmen Steve Smith (134) and Adam Voges (106) were rarely troubled as they added another 206 runs before declaring midway through the afternoon session.
Smith brought up his sixth test century of the year shortly after lunch to an ovation from the 40,000-strong Melbourne Cricket Ground crowd as he and Voges shared an unbeaten 221 partnership.
Voges completed his century shortly after Smith with a drive to the boundary, passing 1,000 runs in a calendar year, finishing with 1,028.
Australia has scored 1,134 runs for just seven wickets against the West Indies so far this series. Australia declared at 583-4 in the first test, when it beat the West Indies by an innings and 212 runs.
Jerome Taylor finishing the innings with best figures of 2-97 but it was a meek effort by an inexperienced West Indies attack. The fielding was no more impressive, with Voges and Smith playing shots all around the field and taking quick runs thanks to some sloppy returns.
Smith hit eight boundaries in his 177-ball knock, while Voges smashed 12 fours from his 166 balls.
Opener Joe Burns scored 128 and fit-again Usman Khawaja had 144 to set a solid foundation on the opening day. Opener David Warner was the only batsman not to score a century. It was just the third time in history that four of the top five batsmen made centuries in a test innings after Pakistan in 2001 and India in 2007, both against Bangladesh.
BRIEF SCORES (FULL SCORECARD)
Australia 1st innings: 551 for 3 declared (Usman Khuwaja 144, Steven Smith 134 not out, Joe Burns 128, Adam Voges 106 not out; Jerome Taylor 2/97).
West Indies 1st innings: 91 for 6 (Jermaine Blackwood 28, Rajendra Chandrika 25; James Pattinson 2/36, Nathan Lyon 2/18, Peter Siddle 2/19).
Australia lead by 460 runs.