I think that double negatives would be allowed but not preferred, much like English. “I don’t love nobody” would make sense, but feels “uncouth” or “uneducated” to me, as it does in English.

Or perhaps "I don't love nobody" would be taken as "I love somebody".

It’s possible, but I suspect, like English, that interpretation would only be likely if the sentence were arranged properly for emphasis: ná laquen ya lá melin “there is nobody that I don’t love”

+Paul Strack Hmm. Or maybe laquen ná ya lá melin

Interestingly, in Hungarian the double negative "I don't love nobody" is the correct choice. "I don't love anybody" means "I don't love just any person [only you etc.]"

+Tamas Ferencz Likewise with Turkish.

+Ekin Gören even a kind of triple negative is perfectly fine. senkit sem szeretek literally means "I don't love even noone"; sem is "also not, not even, neither"

In English a double negative is sometimes used for emphasis: “I don’t love nobody” is stronger than “I don’t love anybody”. But it also perceived as somewhat uncouth speech. It’s tricky, because (in America at least) there is a element of racial politics involved. Double negatives are fairly common and normal in Black English Vernacular.

So my interpretation of Quenya is biased by my own native English language and it’s American usage.

I read in Bill Bryson's book Mother Tongue that the "incorrectness" of the double negative, and many other so-called rules in English can be traced back to an eighteenth century English clergyman and grammarian Robert Lowth who write a book about what he thought was "correct" English, and his book got so popular it for reprinted many times and his ideas stuck.

+Paul Strack laquen ná ya lá melin for me means "There's no one I don't love", i.e., I love everyone)

+Andre Polykanine yes, that was my intent.

+Tamas Ferencz in America at least, double negatives used to be a class thing. Well educated people (upper classes) avoided them and less educated/lower class would use them, but it was generally a speech pattern that was perceived as “ignorant”.

However, it is also a speech pattern common among African Americans, and now (in America) is sometimes perceived as representative of that ethnic group. So this speech pattern “sounds black” to many Americans.

I don’t know enough about it’s origins among African Americans to know how this speech pattern came about. It could have been copied from general Southern American speech patterns, or it could originate in African language speech patterns.

Well, the negative agreement or negative concord (or "the double negation" colloquialy) is an innovation in both Indoeuropean (like English) and Uralic (like Hungarian) languages - while the absence of this phenomenon was the older, original state of things.
So it's no surprise that in the languages where it emerged comparatively later (like English), it's still considered a part of the lower-registry forms of the language (which are always more progressive compared to the conservative "cultivated" forms).

Anyway, as for the presence/absence of negative agreement in Eldarin, I could find only one relevant example. And it's quite interesting.
It's G. "neither flood, nor time stops for anybody": u laud u laith hasta unweg "not flood not time stops-for nobody" >> u laudin laithin hastath unweg "not floods times stop-for nobody".

+Lokyt L. Ooo. That is a good example. It’s stronger hints that double negatives are possible. And they can used, like low-register English, without reversing the entire meaning back to a “positive”.

+Lokyt L. Fantastic find!

Furthermore, the absence of any negative element by the verb (at least in the earlier version of the sentence) places Gnomish of 1917 (if not the later version) within one of two specific cathegories of languages regarding the grammar of negative concord (check https://home.uchicago.edu/~giannaki/pubs/nwords.pdf, chap. 3, if interested). It's the same cathegory as one of Tolkien's favourite real-world languages, Spanish.
home.uchicago.edu - home.uchicago.edu/~giannaki/pubs/nwords.pdf