I believe the spider once invited the fly into her parlour, or was it her parlor? The answer probably depends on whether you're English or American. But the question is, which spelling would you expect in a novel, and what difference would it make.
When a Regency heroine invites the "Honourable Fred" into her "parlour," English readers accept the words (and spellings) without a second thought, while American ones, those attuned to Jane Austen movies at least, hear and smile at a peculiarly English tone of voice. Meanwhile, when the Regency heroine says "parlor" (or "honor"), English readers hear an American voice, quickly setting the scene as somewhere across the Pond... but what do Americans hear? (Or Australians even?)
If it matters that your readers hear an English intonation, it might be good to use English spelling, in dialog at least. But that gives rise to the vexing question of what spelling to use in narration. Is the narrator English or American, anglophile or purist, part of the story or a disinterested observer?
Most readers, of course, won't notice which spelling is used. But the human eye is attuned to "change," so changing the spelling midstory, or even between dialog and narration, will almost certainly attract attention. Will it distract your readers? Will it make them stop to question the voice (or spelling)? Will it draw them out of the story?
Sometimes the narration is a vehicle for the author's commentary, in which case an American author must surely use American spelling. But if the author's intent is invisibility, letting the story absorb readers' attention to the exclusion of the world around them, then the choice of spelling and consistency of spelling become important. At this point the editor, also trying to remain invisible, might ask which spelling the author wants, which voice the author wants the reader to hear, and even, in the case of a series author, which spelling was used in the rest of the series.
Parlour or parlor; the honorable or honourable Fred; debts of honor or honour; color or colour... not all words need to be consistently English or American, but perhaps each individual word should be self-consistent... perhaps. The editor (also trying to invisible) might notice and offers a suggestion, but the author makes a choice. And that's as it should be, at least in this editor's parlor.