Ah, ML, you are a tricky one.
And there were certainly no grungy motel rooms there. And given the peeling paint and the cracked linoleum and the fact that none of their stuff seemed to be here - none of the stuff that normally cluttered up her bathroom - she could only conclude they were in some very cheap motel room.
The shower definitely sounds like it's the motel she and Clark hid in while on the lam.
OK, so on to the next major development ...
“You heard him, gnome! Blow!”
Gnome? Clark looked back at the floating man in shock. Surely Lois must mean that figuratively. “Lois...”
“How’d she do that?” the gnome asked. “You’re supposed to be frozen!”
“Yeah, well, I thawed out. And Clark’s not going anywhere, Mazeltov!”
“Mxyzptlk! Mister Mxyzptlk! Fine! Have it your way!”
Mister Mxyzptlk! Hah! Either you're laughing at us for not considering him as a source, or ...
After all, it was obvious that Tempus was, once again, playing with the past.
Mr. Mixit-up is a red herring and Tempus is really behind this.
Still, since she was here, there was only one choice - to find that stupid Godzilla doll and get back to the Daily Planet.

LOL, you said you were going to torture Lois, but I didn't expect this.
“I hope so. But, still, that’s not nearly as bad as what Clark did.”
“He didn’t do anything different.”
“No? When he left his former self, he was x-raying the building where Lois and Luthor were hiding out. Superman busted in immediately, rescued Lois and took Luthor to jail. Luthor didn’t die in that collapsed building. A few years later, he escaped from prison and many more people died at his hands as he continued his criminal endeavors.”
“Oh god.”
“We have to brace for this quake. It’s going to be huge. By the time it’s over, some of us might not be here - especially if any of us have ancestors who Luthor killed when he continued his terror spree.”

Yikes! Maybe a future jump will change the changed future? Or, if it's Mr. Mix-n-match, everything will go back to the way it was once he's banished, right?
Great chapter ML. Can't wait to be confused some more tomorrow.
BJ