Open any level in Copycat Lemmings, then look at the trapdoor. It is already open. Then, after the "Let's go" sound, the trapdoor then does the opening animation. This is a graphical glitch.
If you open a non-Cheapo-conversion style level, the trapdoor will be shown closed.
EDIT: Or, open a level in Lemmings Reunion / PimoLems that uses styles converted from Lemmini. The same problem occurs.