With all the newly appointed ministers taking up the bulk of the paperwork, Lilith and Michelle could spend more time preparing the dungeon's defenses and nearby territories. This time, even if Samael managed to break through the teleportation block and reach the center, they should have an easier time protecting everyone while handling the intruders.
Ein, on the other hand, left all the work to the girls while he went to the second dungeon. There, he spent time outside with nothing but a single book and practiced his magic in preparation for another bitter fight.
"... Space and time come in pairs. One cannot move through space without moving through time. Moving through time can usually only be done in one direction: forward."
His focus was on preventing Samael from escaping, like last time. Thus, the spells he was trying to learn were more or less focused on spacetime manipulation, of which teleportation was the most basic.