LINNETS' manager Tony Spearing admitted his side were fortunate to get a point after a second half onslaught from newly-promoted Hinckley on Tuesday night.
Chances for sides were at a premium, although Hinckley did have the ball in the net twice only for both strikes to be rule out after fouls on Craig Clark.
Manager Tony Spearing said: "To be fair the referee blew up straight away for both fouls but on another day they might have gone against us.
"I thought we did enough to win in the first half but after the break we got out of jail.
"Too many players weren't at the races after the interval."
Lynn's only shot on target came courtesy of an Adie Hayes free-kick, but other than a late effort from captain David Robinson, who was outstanding in defence, Linnets rarely threatened.
Lynn: Wilson, Dakin, March (Eldridge 69), Robinson, Fuff, Clark, Anderson, Hayes, Rowland, Hudson (Jones 69), Minett. Sub not used: Wright.
Attendance: 405 (Given as 389 in League Bulletin)
MoM: Dave Robinson.