Alec should have blamed the door "opening" on his exhaustion as any other rational being would have, but he didn't. He was not able to.
He could swear, even holding the Soul Sword, that the door opened by itself, and the whole thing was driving him insane.
Lightwood did his best to focus and sadly had little success at it, meaning that the mountain of papers that required his attention stayed critically unattended.
The Head of the Institute took all the piles marked as time-sensitive and left the place without looking back.
Maybe cooking would help him clear his mind.