LGCC will host Broxbourne on Sunday August 13 (1pm) in the Readers Herts County Trophy semi-finals after a workmanlike quarter-final win at Old Elizabethans.
Green set the Barnet-based hosts 251 to win after several batsmen got good starts before getting out.
Miles Barnard top-scored with 50, Kris Jadeja hit 49 and there was 43 from Sol Tomlinson as Levy's innings petered out from 185-3 to 250 all out with 11 balls wasted.
In reply, it was only when OEs' No. 8 Chris Busby (50) joined Matt Holland at the crease that the hosts looked to have even a sniff of winning.
They blazed along above the required run-rate but lost too many wickets in doing so, leaving the middle and lower-order to regroup and eventually post a respectable 192 all out in reply.
Skipper Dayle Littlejohn took four of the wickets to fall, but at a somewhat costly 70 runs from his 10-over spell as Green ran out winners by 53 runs, adjusted down for rain after the loss of one over's play.
Broxbourne beat Kings Langley to set up the last-four clash at The Green, for the right to face the winners of Hemel Hempstead and Knebworth Park in the final of the competition LGCC won - unforgettably - with a leg bye from the final ball of the 100th over two years ago against Abbots Langley.