Lex also entertained, for a brief moment, that Vox might be lying about his power and origin. It was not only possible, it was also plausible. Considering that he wanted to establish a working relationship with Lex, the more he built himself up, the more he would entice Lex to work with him.
Moreover, by explaining how desperate his situation was, in the future when things wouldn't go his way, Lex would have no reason to doubt his identity, because the trouble existed despite having such an identity. It would lull Lex into accepting his identity.
But after some thought, he felt like it was unlikely. He couldn't be absolutely certain, but it still felt like Vox did not need to lie. After all, at 35% power, he was not a weakling, and his position granted him actual power, as Lex had already seen.
