I suspect the only people who can answer this are OUP.

Those are two different sources. The OED was not the source for Lexico/ODO.

From my limited knowledge, the two dictionaries don't seem to share anything other than 'Oxford' in their names. At least that's the impression I got.

The plural of zero is /'zɪroz/. Like all English words, there are many ways to spell this. Which one one chooses is irrelevant, so it's no wonder sources differ. Neither one is right and neither one is wrong. They're just different spellings, not different words.

@JohnLawler It sounds like you are saying it doesn't matter how we spell plurals, or maybe you are rejecting conventions that have established potatoes and mosquitoes vs. "solos" and "avocados."

@GArthurBrown No, I'm merely saying that spelling has nothing to do with English grammar; it's strictly a printing convention. Are you saying that it is important somehow to always spell a word the same way? Why? Who says?

Not that this explains the discrepancy, but OED seems to be on the wrong side of the favored spellings here according to the Ngram

As I said the other day in another post, motivations of lexicographers are off topic.

@JohnLawler Spelling does, however, have something to do with the English Language.

@GArthurBrown If you say so.

Maybe it was Mark Twain that said “Anyone who can only think of one way to spell a word obviously lacks imagination.” Others say it was Nyrum Reynolds, or Hirum Runnels (?)...

There are Oxfordians. And then there are Oxfordians.

I thought that Oxford University Press has been (or was in the past) responsible for both dictionaries, and that's what they have in common at least. Is it not the case?

@AndrewLeach … and some folks from OUP (or some folks knowing OUP well enough) might potentially read here.

@Mitch Well, if you think that's an answer, feel free to convert it into an answer. What you wrote probably means that the publishers did not care about synchronizing their dictionaries or perhaps even intentionally cared about NOT synchronizing them. Perhaps; it's just a guess of mine.

Interesting. Lexico has noun zero plural zeros. But verb zero with conjugation zeroes, zeroing, zeroed.

The two dictionaries each have their own editorial boards responsible for their contents. Why should the publisher try to overrule one or the other?

@GeekestGeek I dont know enough to give a proper answer but looking at different websites should be able to give someone the means to a more formal answer. As to intention, that is presuming quite a lot. The editors are people, probably didn't start from scratch and thought unconsciously that it'd be too much work to try to make a correspondence. Using the name 'Oxford' was purely a marketing decision.

@GEdgar But most people, myself included, would presume that they are somehow related, as does GeekestGeek. Only after encountering consistent differences between the two dictionaries did I realize that the presumption was baseless.

@Mitch Are you sure that using the name “Oxford” was a purely marketing decision? If so, that would constitute an answer (essentially, saying that “the Oxfordians” do not exist or that they are unrelated to the dictionaries).

@GEdgar Are you sure that the editorials boards were completely separate and have no influence on one another and no intention to synchronize, as well as that the publisher had no intention to make stuff consistent? If so, that would probably also constitute a valid answer.

@EdwinAshworth Before the discussion, it was not at all obvious to me that the dictionaries had different editorial boards, that they probably do not speak to each other, that no serious attempts were made to synchronize the dictionaries, and that the surveys underlying the dictionaries were independent. That was all news to me. So, if that's obvious to you, i.e., you are darn sure about it, feel free to convert it into an answer.

@EdwinAshworth As for the editorial boards or anyone knowing them well enough, they might read here and speak for themselves (if they care). I recall asking a language question to ODO/Lexico several years ago; I never heard anything from them, so, I wouldn't be surprised if they wouldn't give a darn replying.

@JK2 So, was no attempt made to make the dictionaries at least somehow agree? If so, that's a pity :-(. It essentially says that OUP does not care or mostly doesn't care about consistency. Sigh. I'd expect the opposite from one of the most authoritative academic publishers worldwide. Is my expectation is too elevated?

'OUP does not care or mostly doesn't care about consistency.' But the boards are independent, which is usually healthier than the alternative. Do all dictionaries in the same language need to compare notes? FWIW, M-W's surveys have led to their judging that both zeros and zeroes are acceptable. And Cambridge Dictionary is inconsistent even within its own article, giving only zeros in one section but both variants in other sections.

@EdwinAshworth How sure are you that the boards are independent, as you wrote? If very sure (say, it's written somewhere), feel free to provide this piece of knowledge in an answer. As for me, a priori I know nothing about their independence or, on the contrary, any mutual influences or even intersections. It is imaginable that (hypothetically) the same folks could get paid for different job in different years.

This is off topic. It is not a discussion about the English language as such, but (your latest request) about how certain connected institutions are constituted. ELU deals with English, not institutional make-ups and policies. I do know that OED for instance has a website answering at least some questions about policies.