After leaving Miranda, Lex had returned to his office and sat there, seemingly looking at nothing. His connection to the Inn through his attire and his chair kept him updated on everything that was happening, while he tried to address his current mood. Truth be told, he was feeling ambivalent.
His family had not deigned to include him in their secret, yet here he was, searching out for his sisters. Although he didn't blame his sisters, he also could not help but feel betrayed. A part of him just wanted to go and confront William and get the truth. But a part of him also just stopped caring.