Kyle Mayers, who has been ruled out of the remaining two Tests due to a shoulder injury, added only 10 runs to his overnight nought. Lyon broke through when Mayers got a hefty edge on Steve Smith at slip.
Part-time spinner Travis Head was introduced at the other end and dismissed Jason Holder for three in his first over, with Smith collecting a brilliant slip catch.
Australia took the new ball, along with their pace batteries. The West Indies were in trouble after Josh Hazlewood tempted an outside edge from Joshua Da Silva, which Usman Khawaja gathered at second slip.
But Rostan Chase (43) and Alzarri Joseph (43) fought back, contributing 82 runs for the ninth wicket before Head bowled Joseph to end the partnership.
The West Indies were never able to recover from Australia's stunning first innings batting effort, which saw Marnus Labuschagne and Smith both hit double centuries to drive Australia to a mammoth 598-4 declared.
After the West Indies were dismissed for 283 in reply, Labuschagne hit 104 not out to become only the eighth player in Test history to achieve the 200-100 feat, following Sunil Gavaskar, Brian Lara, and Kumar Sangakkara.
While outplayed, a young West Indian team demonstrated tenacity and determination.
With injuries mounting, the West Indies addressed an SOS to uncapped Marquino Mindley, who is on his way to Australia to cover the Adelaide Test.
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