Keep in mind that Zack Snyder left the production before it finished filming. It was mostly done, but the actors were still around for re-shoots and filler scenes. Whedon was brought in to finish it up, and wound up completely re-shooting most of it. Some of the discontinuities may be because of scenes Snyder was planning to shoot, but didn’t have a chance to, and which Whedon abandoned when he revamped the whole thing. That being said,
Lois is a world-famous journalist. Her work makes a difference in peoples’ lives. Her investigations uncover and expose wrong-doing, and her writing bridges divides by providing understanding and hope. MM, an alien but deeply compassionate and perceptive observer of the human condition, realizes more than Lois herself does just how important she is to the world.
There may have been a bridging scene missing here. IIRC, in the Whedon version, she sees news coverage of Superman’s return, and the implication is she knows her son better than anyone and knows he’s going to head home, so she goes there as well. Or maybe Lois called her. Or maybe Bruce did.
This is a real hole in the Snyder cut. Martian Manhunter’s plan only really works if Lois and Martha never talk again. If they do, they’re going to figure out pretty quickly that something really weird happened. MM is practically gaslighting Lois.