Same result, same scorer for the second game in succession for the Linnets.
Lynn striker Danny Bloomfield again popped up in the first half to notch the only goal, this time a penalty.
The Walks outfit fielded the same team as the win over Bedford five days previously, except for Dean Whittaker making his debut in place of Cedric Anselin.
Whittaker is definitely in the Peter Crouch mould, tall and gangly, and it was he who earned the spot-kick for fellow front man Bloomfield, the "Little" in the "Little and Large" partnership.
On the win, which lifts Lynn up to 12th in the table, manager Tommy Taylor said: "We did alright in the first half, but after the break we didn't keep the ball enough. Once again we should have had the match wrapped up by the break.
"They were a big side and that's why I kept Dean Whittaker and Jack Defty on, despite the two of them being tired, to cope with their threat in the air.
"The boys at the back did well. Cheshunt had 12 corners in the last 20 minutes but we dealt with them."
In the first-ever league meeting between the sides, Lynn bossed the first 20 minutes, but their finishing was poor.
Grant Cooper, who never misses an opportunity to go forward, on the quarter-hour mark unleashed a tremendous 25-yard effort that the home keeper Martin Peat was nowhere near, but it cannoned off the left-hand post.
Dean West, Jack Defty and Sam McMahon all had shots inside the Ambers' box, but all off-target.
Cheshunt showed little in the attacking department, apart from a spell between 20 to 30 minutes when John Higgs dealt comfortably with two shots from Lloyd Opara.
Bloomfield played in Defty on the left of the hosts' area but the midfielder fired his right-foot shot well wide of the post.
But shortly after, in the 35th minute, a challenge on Whittaker earned that penalty which Bloomfield confidently placed in the keeper's right-hand corner.
Referee Mr Ross confirmed after the game that the spot-kick was awarded for Ryan Bernard's clumsy tackle from behind and push on Whittaker.
As expected, Cheshunt came out in the second half wanting a reply, but despite having a lot of play (and a host of late corners) they threatened little a defence which was well-marshalled by Cooper and Martin McNeil.
They lapped up some one-dimensional play, with the Ambers content to just ping the ball into the penalty area.
At the other end, Defty and Whittaker combined to set up Bloomfield, who fired over the top on the hour, while five minutes from the end sub Paul Kelly missed a sitter, Defty again the provider.
Cheshunt: M. Peat, D. Fenton, G. Parry, N. Gyoury, D. Reddington (M. Deane 70), R. Bernard, A. Fenton, L. Allen, G. Gregoriou, L. Opara, B. Highton (S. Obeng 77).
Subs not used: R. Tungatt, L. Patrick, M. Kalli.
Lynn: Higgs, West, Camm, McMahon, Cooper, McNeil, Jones, Whittaker, J. Defty, Bloomfield (Kelly 75), Smith.
Not used: O'Halloran, Anselin, Tjirimuje.
Referee: Mr J.J Ross (Chingford).