Chasing an unlikely 416 for victory, the Black Caps were skittled for 136 with off-spinner Lyon taking five for 50 and Mitchell Starc claiming three for 25.
Number seven Colin De Grandhomme top-scored with 52, while Ross Taylor became the Black Caps’ highest Test run-scorer during his knock of 22.
FULL SCORECARD: Australia vs New Zealand, third Test at the SCG
The 35-year-old, who has played 99 Tests, overtook Stephen Fleming to move on to 7,174 runs.
David Warner set up Australia’s victory push with an unbeaten 111, sharing stands of 107 and 110 with Joe Burns and half-centurion Marnus Labuschagne respectively, as his side declared on 217 for two.
Australia were penalised five runs during their second innings by umpire Aleem Dar as a result of Warner and Labuschagne running on the pitch.
Hales lost his place in last year’s World Cup-winning squad after news of a second failed test for recreational drugs.
The Warwickshire all-rounder is one on 18 bowlers to be selected for personalised practice.
The West Indies are due to arrive on these shores first this summer.
Broad took part in an individual training session at Trent Bridge.
Clare Connor suggested England are considering hosting a Women’s Tri-Series also involving India and South Africa.
The designated bowlers, whose identitites have not been confirmed, will have their temperatures checked.
The ECB had planned to introduce 40 professional contracts this summer across eight regional hubs.
County are waiting on a decision.
The Somerset bowler last month opened up about his mental health struggles and he discussed the topic further with Marcus Trescothick on Zoom.