It was a well known and established fact that Lex was not greedy and was, instead, a humble fellow who had given up his attraction to worldly possessions. The fact that he hoarded dozens of armors in his spatial bangle did not go against this fact, as those were there to serve a functional purpose.
He wore no jewelry or expensive watches, and did not have an expensive shoe collection. Even back when he was a mortal and made 7 million dollars, he did not waste it all and instead invested it. He continued to work at his job in the meantime, and lived a normal life. Yes, Lex was a proverbial monk. His only interest in any treasures the facility hid was purely academic and if, god forbid, the facility were to ever fall to the invaders and Lex intervened, it was only out of a sense of honor and duty. It was his duty as a man, no, as a human, to ensure that the alien robots failed in their objectives.