She had to have a personal object of theirs to control them, and she didn't have anything that belonged to Lex. That's what I've put it down to now, and also possibly that she isn't aware that Lex has mutant abilities, so she had no reason to try and swipe something to control him. Honestly? Probably clumsy writing/continuation, but I think it's actually reasonably solid reasoning if you put that aside and ignore that Chloe should know about Lex being a potential mutant, and could have thought to try and swipe something of his.

Although then I don't think the case file specified that Moira needed a personal object? Though I'm not sure, I'd have to rewatch and check. So Chloe would have had to know before Lex's men grabbed her, because her best bet probably would've been to go visit Lana and grab something from the mansion. I don't remember them having a chance to grab something of his after Chloe was kidnapped though.

Also, I could be a little fuzzy on the timeline, but I think he went to see Moira post-car accident and his face was healed, when it was cut up when he saw Lana that morning. I'd have to rewatch and double check, but I'm fairly sure it was cleanly healed, and there was a bandage-type thing there when he saw Lana so there was some kind of surface damage. I took that as Lex healing really quickly, because Moira had a short time-frame on being lucid.