I mean, the shirt fits. He knows that he needs help with suburban women and he sees her as the spitting image of one. And just like him, she's an attention whore and a loser who insists she's a winner.
Nimrata ain't getting it, or anything in a second Trump admin; she's fishing for a book deal and/or a talking head gig by posturing herself as a voice of reason. Noem came roaring onto the national stage as the DeSantis of the Plains, but her profile has since faded somewhat despite a resounding re-election in which she quietly gained 11 points over her 2018 results. South Dakota is just too small, too white, and electorally irrelevant for her to maintain major media attention. She doesn't have the knack for soundbites and camera presence that Lake naturally has as an ex-journo turned conspiracy pimp and provocateur. Or at least, Noem doesn't seek those opportunities out.
Trump is not smart, he will be drawn to his fellow megalomaniacal nutjob whom he will admire as a "fighter". Lake lives in an actual swing state and loves media air time, regardless of the fact that she herself lost a close election there in large part due to her *ahem* charming personality. Plus, given that she rose in the TV journalist ranks during the 90s, she presumably knows how to fall in line, schmooze male bosses, and cheerlead like she's told.