It's the fifth time in eight seasons Lynn have crashed out of the FA Cup to a northern side, but The Walks outfit were very unlucky not to come away from the Giant Axe stadium with a replay.
They went behind during an even first half and played their best football for some weeks, but again lacked a cutting edge.
Lynn caretaker boss Robert Taylor said: "We could have won it, we had enough chances. We conceded an early goal again.
"I changed it around a little bit in the second half and we were different class, we had a lot of possession.
"But their keeper had a good game, and we just needed a rebound to go on off someone, it was one of those days."
Of the new boys, he added: "Ryan Clarke did well, as did David Staff up front."
Danny Hammond (at left-back) and Gary Setchell made their first starts back in the side's defence after injury, allowing Adam Jones (right-back) and Mark Camm (midfield) to slot into their natural homes. Jack Defty was on the bench following news of a family bereavement before the game.
Centre-half Ryan Clarke had an excellent debut, while fellow on loan player David Staff - a welcome sight back in Lynn colours - tried a couple of trademark free-kicks to no avail.
The underdogs opened up the better side, Mark Angel going past two defenders but shooting straight at keeper Jamie Speare, who had an inspired day between the posts.
Following a delay caused by treatment to home captain Gary Bauress, who fell awkwardly, Jamie Murphy headed wide a corner. But City soon went ahead.
Steve Jones switched play from left to right to full-back Ryan Elderton, who fired home under Steve Wilson's arm.
At the other end, Hammond's shot was saved and on 20 minutes the ball bounced just right for Carl Holmes, whose fiercely-struck effort hit Speare on the chest.
On the half-hour mark Peter Thomson, who looked well offside, hit the base of the post, while Elderton almost added to his tally as his dipping effort just cleared the bar.
The Linnets dominated the first 15 minutes of the second half, but the final ball was lacking. Eight minutes in, Danny Bloomfield lost his marker and let fly, however Speare dived to his right to save well.
Lynn's Jones pushed upfield from just inside the home half and had an effort saved, while Holmes' header was the wrong side of the post.
The visitors had one scare when Steve Jones headed a corner goalwards, but substitute Lee Stevenson cleared it off the line.
Taylor threw on all three subs and Staff tried his luck from long range, but Speare had the last word with a save.
Lancaster: Speare, Elderton, Scott, Sparrow, Murphy, Hollis, Bauress (Clark 29), Jones, Thomson (Barry 90), Zico-Black (Sullivan 76), Prince. Subs not used: Yeomans, Urberschar.
Goal: Elderton 13.
Lynn: Wilson, Jones, Hammond, Camm, Clarke, Setchell, Holmes, Fishlock (Stevenson 55), Staff, Bloomfield (Harris 85), Angel (Defty 76). Subs not used: Higgs, Harvey. Booking: Setchell 83, foul.
Att: 318. Referee: J. Collin (Liverpool).