Great beginning! I, also, welcome you to your first official posting on the boards and your first story.
I wondered at first why Clark was avoiding his own apartment, having completely forgotten the lack of privacy he had at home with all of his house guests.
I agree that Lois usually has better judge of a person's character than she had with Luthor. I mean, she did accept Superman right off the bat, no questions asked. Okay, that might be the only good example. She was suspicious of Clark from the get-go, but then again, she had been burnt by co-workers before. And, in her defense, Clark was lying... er... omitting a very important detail about himself from their friendship and maybe she could sense that (sense that he was holding something back). She knew that he withheld information from her (i.e. the globe, his undercover assignment at the Star, his biggest secret -- per their discussion from Ides of Metropolis -- just to name a few) and maybe she could sense he was still holding back. Although, that doesn't explain why she wouldn't trust his opinion on Luthor. Did she naturally think just because he could be jealous of the billionaire that he would change his personality and start lying to her?
I could see that those words and her actions to Clark on the park bench (and towards Superman right after) and refusing to believe his warning about Luthor, especially after what he had just dealt with in the cage, would continue to upset him. He deserved better from Lois and some acknowledgement that he was "right" this time.
Clark, somewhat, gets back at Lois in Madame Ex by not believing her when she says that someone was impersonating her. After all, not only does he have a quite believable impersonator working in the city (oh, wait, he doesn't know about Barry, yet), but he also had the clone try to replace Superman not too long ago. They certainly have some work to do on their friendship to rebuild their trust.
His natural tendency is to run away from personal confrontation, so him retreating to a lone hotel room to lick his wounds makes sense. I'm glad that he had the decency to let everyone know that he was safe, not that they seemed too worried about his disappearance. I do think you nailed Jonathan and Martha's helicopter parenting in this part. They do seem to drop everything to fly out to Metropolis often enough.
I, too, am curious to see where you'll be taking our favorite characters. Clark is certainly suffering from ambivalence at this point in their relationship. Will Lois bend her stubbornness enough to admit that she was wrong or to thank Clark for trying to warn her?
I wish you luck in finding a beta. My spare time is zilch nowadays, but I'm pretty good at nagging people to post the next part.
If you create the FDK post to accompany each part (make sure that you click the box that says "Add Topic to my Watched Topics" or you can also follow this one by doing the same. Click on "Topic Options" and scroll down to and click on "Add Topic to Watched Topics") you'll get an email announcing every time someone posts to that thread.