Wait and watch
Lex observed the spirits in trench coats for a while, but when they did not seem to be doing anything suspicious, he let them be. He did, however, turn his attention to the lightning tribulations. After isolating the abodes, Lex had not paid much attention to the tribulation, for they never really struck anyone other than their main target. Even the massive spaceship did not seem to be an obstruction, as wherever the ship was an obstruction, the lightning clouds would just form under it.
But it seemed like he could not just let them be. After all, since he was instructed to create a tribulation room, and it would become an eventual facility, he should get it done as quickly as possible so the maximum number of guests can benefit from it.