Earlier, Australia vice-captain Steven Smith fell one short of a double century as the tourists reached 399 all out during the afternoon, with Jerome Taylor taking career-best bowling figures of 6-47.
However, the Windies got their innings off to the worst possible start, losing the wickets of Rajendra Chandrika, Kraigg Braithwaite and Darren Bravo cheaply before tea.
Things did not get any easier for West Indies after the start of the final session. Shane Dowrich (13) could only edge a Josh Hazlewood (3-15) ball into the hands of keeper Brad Haddin before Shai Hope was bowled for 26 by Lyon (3-35).
Hazlewood took his second wicket when he trapped captain Dinesh Ramdin lbw for just eight, but a steely half-century from Jermaine Blackwood gave the hosts hope of getting the deficit under 200 runs.
However, the New South Wales quick bowler removed the Jamaican right-hander before Mitchell Johnson (1-38) snuffed out tail-ender Veerasammy Permaul to leave the Windies foundering at 143-8 at the close.