THE Linnets maintained their 100 per cent record in penalty shoot-outs in this competition on Tuesday.
A rainy Walks saw Lynn sub Seamus Kelleher score before a Tudors late leveller.
With no further scores in extra-time, the shoot-out saw Lynn convert all their spot-kicks, but Chris Dillon – who Lynn turned down recently – missed his to send The Walks outfit through to the last eight.
Lynn boss Keith Webb said: "We deserved it, and had chances to wrap it up. We were a bit fortunate when they hit the post.
"It was a chance to experiment with a few different shapes. When we switched from 4-3-1-2 to 4-4-2 we looked more positive.
"Our penalties we looked to approach positively. Seamus did alright when he came on and looked lively. Kieran Deane did better when he went from the centre to out wide."
A young Lynn side had only Charlie Defty remaining from the 11 who started Saturday's game, against a strong-looking Hemel outfit.
Within 90 seconds of the start, Mark Heath-Preston hit the top of the bar with a fierce 20-yard effort.
Hemel – sporting a Quality Street green shade of kit – had their first chance on ten minutes when Aaran Cavill fired wide.
Heath-Preston was denied by keeper Sam Styles' legs, while Andrew Fisk fired wide.
Five minutes after the break Drew Roberts skipped past Defty and hit the far post, but the ball rebounded straight into home keeper Rob Murray's legs.
Heath-Preston and Matt Nolan went close before Kelleher bagged his first Lynn senior goal, a tap-in after John Turner shrugged off Chris Herron and drew a save from Styles.
Lynn had chances to wrap up the game, but with three minutes to go Harry Hunt equalised, flicking home a left-wing cross.
Yiadom Yeboah cleared a Fisk header off the line, and Fisk could not convert following a poor back-pass.
In extra-time Styles smartly saved from a Kieran Deane long-range effort, and a Deane free-kick cannoned off the post. Dillon had the Tudors' best chance, but sent his overhead kick too high.
The Walks outfit were confident in their spot-kicks, while Dillon's weak penalty going wide was the telling factor.
Lynn: Murray, Harvey, Lake, C. Defty (Miller 105), Buhlemann, Melton (Carey 75), Deane, Fisk, Nolan, Turner, Heath-Preston (Kelleher 65). Subs not used: McAnally, Keegan.
Booked: Fisk 45+1, Kelleher 79, Deane 96. Goal: Kelleher 69.
Hemel: Styles, Champion, Coulson, Herron (Nicholls 73), Bowden-Haase (Yeboah h-t), Jackman, Gearing (Hunt 63), Cavill, Dillon, Roberts, Edgeworth. Not used: Wood.
Referee: M. George (N. Walsham). Att: 385. MoM: Charlie Defty.
Penalty sequence Lynn: Fisk, Deane, Turner, Miller, Nolan.