Some rules state (possibly Lulu's!) that changes to any publication with an ISBN will require a new Project and new ISBN. I even tell people that!
But most publications do change, but keep the same ISBN.
I do not mean a new shape and size or cover etc, or publisher even, or changes to the actual 'story' text, but what I do notice changing in most long running publications is a change on the Also By This Writer, and Also By This Publisher page/s, and web addresses and other contact details, but the ISBN remains the same.
So is there some ISBN rule somewhere that says > "... but you can change ..."?
Yes. It has to be a significant change.
I would have thought that the change of a whole page is significant.
A change of publisher would definitely have a new ISBN as the ISBN identifies the publisher as would a change of format, but if the cover stays the same then its just a reprint which takes the opportunity of correcting out of date details.
It cannot be just due to the cover and I would have thought that a reprint is just to print the next batch to be ready for further orders? (Non-POD that is), not the opportunity to change out of date details in, say, a text book. Would that allow me to change details in a S fiction book based on newer discoveries? I doubt that.
But I'm interested how you have tracked this -- are you buying new copies of books you already have?
Oddly, at times, yes. 
My son is an obsessive collector of SF books and often I have no idea what he has until I buy it again, and he then says he already has it, and vice versa sometimes.
Q:I am revising a book. Does it require a new ISBN?
A:A (substantial) change of text requires a new ISBN, and if revisions have been made the back of the title page should state that the book is a revised edition, and the new ISBN should be printed there.
Usually it says it on the front cover also, if not then people who already have the older one would not buy the newer one, so that would be substantial and would in fact not be the same book.
Q: Does a reprint without change of text, or binding require a new ISBN?
A: No. The original number must be retained.
Indeed, but that does not cover my point about the updating of, well, 'adverts' within a book, which most companies do seem to do, but with the same ISBN. Seems to be a bit of a grey area. What I have now started to do is just put my web address in, which never changes.
Speaking of new ISBNs, I have a book that I published via a print-only site, which they assigned an ISBN to that printed edition. If I want to sell the book here as an eBook, do I simply update the PDF and choose a new, Lulu-assigned ISBN for the eBook/digital version?
You would have to have a different ISBN anyway, regardless of where it is created, because it is an ebook.
