The Warwickshire all-rounder, who has scored two LV= County Championship hundreds this year, added to half-centuries for Eoin Morgan and Samit Patel, the latter of which was completed during day two.
His 190-ball innings with 11 fours was crucial in a Lions recovery from 223 for seven in the final over before lunch on a turning pitch, sharing 75 inside 29 overs for the sixth wicket with Patel and 64 for the ninth with Stuart Meaker.
But the Australians bossed the evening session as Test opener and A side captain Ed Cowan finished the day unbeaten on 77 off 126 balls in a score of 127 for one from 39 overs. He shared 111 inside 36 overs for the second wicket with Michael Klinger, who finished 36 not out.
Woakes, 23, was particularly strong down the ground and playing off his hips as he took his first-class average for the 2012 summer to 88.6 having scored 443 runs from nine innings. Mitchell Johnson led the way with the ball for the tourists by claiming four for 47 from 26.1 overs in only his second first-class appearance since last November due to injury.
The left-arm swing bowler, who has been blighted by a foot problem, bowled with impressive control as he added the wickets of James Tredwell and Woakes to his first-day scalps of Joe Root and Morgan.
He sent Tredwell's off-stump cartwheeling before wrapping up the innings by having Woakes superbly caught by a diving Jackson Bird at mid-off. Bird took both new balls and provided able assistance to Johnson, especially during the morning session when he had Patel caught at first slip by Peter Forrest for 55 and James Harris lbw on the stroke of lunch.
Having opted to bat first, the Lions would have been hoping for a score closer to 400. But having lost three wickets for the addition of 63 runs in the morning after starting the day on 140 for four, they will have been delighted to post in excess of 300. Cowan, however, was the chief instigator in making sure the hosts ended the day on the back foot.
After losing opening partner Liam Davis lbw as he played across the line to Meaker in the fourth over, Cowan was punishing square either side of the wicket as he brought up his half-century off 80 balls.
Klinger settled following a slow start and took a liking to Simon Kerrigan's left-arm spin. He hit him for straight sixes in the 28th and 32nd overs and a four over mid-wicket in between.