A firebrick lid is sensitive and has to be handled as gently as you would a computer or TV set.
It is possible that the lid was handled roughly in shipping--even if the lid looked perfect when it arrived. It can also crack if it is closed too hard. If the crack is near the hinge, it is possible that it was pressed downward before the lid support was fully disengaged.
When the lid is cold, does it have any play in the hinge? You can tell by grasping the upper hinge section attached to the lid and lifting. That play prevents the lid from binding against the kiln as the bricks heat and expand.
Minor cracking around the edge will not affect the firing.