Paul, at this point I’d be casting around for an excuse *not* to delete that leftover laevo. For example, if there is any logical break in the sequence of topics, or any other reasonable pretext, I would put some kind of graphic or marker on the otherwise-blank page. (It is standard practice for a new chapter to begin on a right hand page (recto), even if the facing page is blank, so this isn’t such an outrageous idea.)
Assuming that’s not possible:
InDesign assigns the corresponding master pages to the left (laevo) and right (recto) pages of each spread. It applies the master to the *page*, not to the *content*. When you remove a single page, then, every subsequent page is now on the opposite side. What was a recto has become a laevo, and vice versa. That’s the way InDesign works.
The first workaround that occurs to me is to set up a second master spread as a mirror image of the original, so that what currently is on the left page goes to the right and what was on the right goes to the left. That’s the kind of thing you can do in a layout that would never work in politics. But I digress.
In the pages panel, select all the problem pages (click on the first one, shift-click on the last one). Apply the new master to them in one shot by picking “Apply Master to Pages…” from the Pages panel flyout menu and choosing your mirror-image master spread.
For the future, you can avoid running head issues like the one you describe. Extend the author name text frames the full width of their respective pages. In the paragraph style for the author name, go to the Indents and Spacing section and select “Toward Spine” or “Away from Spine” from the Alignment dropdown, depending on where you want them to appear. You can do the same with page numbers and other items that must be placed toward or away from the spine. In your particular scenario, you’d have two text frames, one directly above the other: one for the page number and one for the author name.