Matthew Wade's maiden Test century had led Australia, who lead the series 1-0, to a first-innings total of 328 after they had been 169 for 7 on the first day.
After West Indies off-spinner Shane Shillingford had done the damage with a six-wicket haul, his best ever Test performance, it was the turn of Australia's main spinner Lyon to make the breakthroughs.
He removed West Indies opener Adrian Barath for 29 and Kieran Powell, who had looked well-set on 40, as well as wicketkeeper Carlton Baugh.
The turn offered by the Windsor Park track allowed occasional spinner David Warner into the attack and he removed Darren Bravo just before tea, a blow which West Indies failed to recover from.
The home side's problem were not limited to playing spin though - skipper Darren Sammy getting run out for 10 as West Indies looked in danger of following on.
As so often, it was Shivnarine Chanderpaul [ Images ] who provided the resistance. He reached 34 not out by the close, supported well by Ravi Rampaul (24 not out) as a much-needed 45 run partnership gave the hosts some hope.
Australia (1st innings):
E Cowan lbw Rampaul 1
D Warner c Powell b Shillingford? 50
S Watson c Deonarine b Watson 41
R Ponting c Sammy b Shillingford 23
M Clarke c Barath b Shillingford 24
M Hussey c Sammy b Shillingford 10
M Wade c Bravo b Shillingford106
R Harris c Baugh b Roach 4
M Starc run out 35
B Hilfenhaus b Shillingford 19
N Lyon not out 0
Extras: (b-4, lb-6, w-3, nb-2) 15
Total: (114.5 overs) 328 all out
Fall of wickets: 1-1, 2-84, 3-105, 4-142, 5-157, 6-164, 7-169, 8-226, 9-328, 10-328.
Bowling: Roach 23-5-72-1 (nb-2), Rampaul 24-6-65-1 (w-2), Sammy 21-7-48-1 (w-1), Shillingford 42.5-9-119-6, Deonarine 4-0-14-0.
West Indies (1st innings):
A Barath c Cowan b Lyon 29
K Brathwaite c Harris b Hilfenhaus 0
K Powell b Lyon 40
D M Bravo c Cowan b Warner 10
S Chanderpaul not out 34
N Deonarine lbw b Harris 7
C Baugh c Cowan b Lyon 5
D Sammy run out 10
S Shillingford b Starc 0
R Rampaul not out 24
Extras: (b-1, lb-1, w-1, nb-3) 6
Total: (65 overs) 165 for 8
Fall of wickets: 1-1, 2-62, 3-73, 4-85, 5-96, 6-103, 7-120, 8-120.
Bowling: Hilfenhaus 11-4-15-1, Starc 10-4-21-1 (nb-2), Harris 9-0-27-1, Watson 4-0-12-0, Lyon 24-5-49-3, Warner 5-0-21-1, Clarke 2-0-18-0.