Linnets regretted not sewing up this game by half-time and had to settle for a point in their first game of the season.
After making a flying start to the new campaign, Dave Taylor notched a goal on his Linnets' league debut. Only finishing which was as reliable as an England batting order prevented Lynn enjoying a healthy halftime lead. In the second half Lynn could not register a shot on target.
Lynn boss Gary Mills said: "We were superb in the first half-hour, but after that we stopped passing the ball. With better finishing we could have been 3-0 up at half-time.
"I was very pleased for Dave Taylor, he's only been with us the last couple of games. I gave him the shirt because he looked sharp."
A bright Lynn first half performance matched the sunny weather.
After just a minute Mark Turner went close with a header from Tony Marsden's cross. Away defender Mark Albrighton cleared the impressive Simon Dakin's shot off the line following a Jeremy Goss free-kick. Then Marsden nodded Dave Puttnam's free-kick inches over.
Tony Spearing scrambled Lee Middleton's comer off the line, but Lynn got their reward on 25 minutes. In a lovely move Lee Wilson found space on the right, centred to Taylor, who spun his marker Paul Olner and slotted past keeper Steve Mokler.
On the half-hour Mark Turner should have doubled the advantage when beating the offside trap as Goss put him through. But Turner's effort was superbly denied by Mokler.
However Linnets lost their way in a second half downpour. Within 10 minutes former Brighton forward Stuart Storer's clever chip found the unmarked Paul White, who nodded past a stranded Chuck Martini. As the visitors upped the pressure Dakin blocked Storer's drive on the line.
Adders' Kim Green wasted the best chance to win it, blazing over from six yards following good work down the right by Richard Barratt.
With a minute left Goss's freekick eluded three outstretched Lynn bodies. So near, yet so far
Lynn: Martini, Dakin, Spearing, Robinson, Clark, Marsden, Turner, Goss, Puttnam (McGinty 84), Wilson, Taylor (Keeble 62). Sub (not used) Fuff.
Atherstone: Mokler, Blair, Barratt, Olner, Albrighton, Redgate, Green (Vincent 90), White (Orton 74), Stoner (Kelly 90), Middleton, Martin.