The hosts, replying to Australia's first innings total of 311, were cruising at 230-4 before Lyon's intervention left them limping to close at 252-9, still behind by 59 with two days remaining.
Lyon finished with 5-68 off 29 overs.
The hosts, overnight 49-3, were led by veteran Shivnarine Chanderpaul's typically composed 94 while fellow Guyanese left-hander Narsingh Deonarine stroked 55. The pair added 130 for the fifth wicket either side of a lengthy rain delay before Lyon changed the course of the day in the final hour and a quarter.
Lyon claimed both and ripped through the tail end in registering his second five-wicket test haul.
The day had a bizarre start with the match officials taking the players off the field under sunny skies just as play was about to commence due to a power outage to the TV production. There was a 20-minute delay to the start as the ICC umpires and match referee chose to wait until technology for the Decision Review System (DRS) was up and running.
Chanderpaul and Darren Bravo began brightly for the West Indies once play got under way. Chanderpaul had an early let-off, on 8 when his edged drive off Lyon deflected off wicket-keeper Matthew Wade's leg before being dropped at slip by Michael Clarke.
But the two left-handers quickly stretched their stand to 62 with an array of eye-catching strokes.
Bravo, in his first test on his home turf, struck five fours off 94 balls before the part-time swing of Michael Hussey gained the breakthrough. The left-hander played inside the line of an inswinger and was lbw at 100-4.
But Australia's momentum was quickly quelled as Chanderpaul found another confident ally in Deonarine. The pair took the hosts to lunch at 132-4 and continued to blossom after the break. Chanderpaul reached his 50 off 140 deliveries, and celebrated by lashing pacer James Pattinson for three boundaries in one over.
Deonarine, who began slowly, also found his range using his feet to attack the spinners.
Heavy rain stalled the West Indies' progress at 188-4 and caused a delay of nearly two hours. But the Chanderpaul-Deonarine association continued confidently even with the arrival of the second new ball.
Deonarine got to his half century, off 132 balls, with a gorgeous cover drive for his sixth four.
But the match was turned on its head once Lyon came back to remove Deonarine with the first ball of a new spell. Deonarine, stumped by wicket-keeper Matthew Wade, struck seven fours and a six off 139 deliveries in just under three hours.
Chanderpaul, in sight of a 26th test ton, departed one run later, lbw as he played a tentative prod. Chanderpaul's innings spanned 217 balls and 297 minutes and was spiced with 10 fours and a six.
Lyon then ripped through the lower order to leave Australia buoyant. Captain Darren Sammy holed out to long-on, Shane Shillingford prodded a bat-pad catch to short leg and Kemar Roach tickled a leg-side catch to Wade.
Carlton Baugh hit an unbeaten 17 and last man Fidel Edwards also survived to close on 0 not out.