For the second season running Green broke the home side's hearts with a Christie Park goal which helped his side to another away point.
Green scored with seven minutes to go when he let fly with a left-foot shot from the edge of the area that beat Morecambe keeper Barry Roche low to his right.
After being on the back foot for so long the visitors then came close to taking all three points when a late Dany N'Guessan strike beat Roche low to his left but came back off the foot of the left-hand post and Adrian Patulea was inches away from then converting a low N'Guessan cross.
Morecambe controlled the early stages with skipper Jim Bentley giving them an 18th-minute lead with a header from Craig Stanley's free-kick.
Dave Artell was then denied a second Morecambe goal a minute later as Rob Burch saved superbly.
But while Morecambe were on top for long periods, Lincoln looked sharp on the break and home keeper Roche also made smart saves to deny Anthony Elding and the excellent N'Guessen who both broke free of the Shrimps defence.
The Red Imps also wasted a golden chance to equalise when defender Janos Kovacs headed wide from five yards out when he looked certain to score from Scott Kerr's left-wing free-kick.
Shortly after the break Morecambe's Michael Twiss ran on to Neil Wainwright's throughball and it took a saving tackle from Moses Swaibu to prevent him making it two goals in successive games.
Morecambe continued to pile on the pressure with Fraser McLachlan firing wide but, as the game wore on, Lincoln grew stronger as the Shrimps lost their shape with injuries to Stanley and McLachlan before Green then stunned the home supporters.