But you and I are modern and we're talking chivalry. That we can talk about it, and non-D&D gamers too, shows the word still gets usage and so there must be a shared definition.
A couple of comments.
First, in my view Wittgenstein and Putnam have fairly convincingly shown that common usage doesn't depend on shared definitions. In the case of "chivalry", I think we rely heavily on shared paradigms. For posters on this board, I would think that Aragorn from the LotR would be one of those paradigms. Perhaps also Arthruian romances, but different people have come to those through many differing paths.
Second, that anthropology and history are possible shows that modern people can grasp, to some extent at least, values they don't share. And I also think that some values can change register - I don't think chivalry is an ethical value for many modern people, but the current fondness for fantasy and mediaeval romance suggests that it has some role as a type of aesthetic value. This may be related to nostalgia and anti-modern reaction, but I'm not sure that's all that it is.
The way I see it, if chivalry is about anything it is about ideals. Ideals of honour, ideals of virtue, courtly love etc.
Oh I can see a certain disdain towards the masses creeping into the code, although I'd treat with care such a definition. It sounds like a definition that served a particular purpose in history. Certainly it is not a publicly acknowledged ideal if only for its ugliness.
I don't think it's seen as especially ugly by its proponents. Aristotle happily argued that many people - including but not limited to women and non-Greeks - are slaves by nature. Roman law takes for granted that justice is each getting his/her due, and that what is due to one of the worthy is quite different from what is due to a slave.
One characteristic of the meek is that they lack honour. Although they may exhibit a certain dignity fitting their station. (In AD&D's UA, this is displayed by the prohibition on leather armour, polearms etc that cavaliers are subject to. Most samurai gaming systems with some sort of honour mechanic will likewise reflect this eg your samurai will lose honour if s/he ends up doing manual labour.)
These are spaces for non-LG paladin to exist within a single class. Become disdainful towards the weak, that's the good-evil axis moving.
But this already reframes the issue. The chivalrous person is not disdainful of the weak. S/he gives them their due. It's just that what they're due is different from what an honourable person is due.
The basic issue, as I see it, is this. Chivalry is not an egalitarian code. And Lawful Good, in D&D, is defined in egalitarian terms. (Although exactly what is to be equal is obscure - sometimes welfare, sometimes rights, sometimes regard, sometimes more than one of these at the same time.)
Over-indulge in personal glory at the expense of duty, that's the law-chaos axis moving.
Again, part of the issue here is that part of being a chivalrous person is honouring one's duty to oneself, and that includes a certain sort of duty of glory. It is not befitting an honourble, chivalrous person to hang back and live in the shadow.
A character like Galahad might perhaps be seen as a limit on this - but even Galahad is
in fact glorious in what he does.
Anyway, I still don't see what the alignment classification is adding to our characterisation of the chivalrous knight. All we get is the risk of the chivalrous Lancelot being deemed evil and chaotic because he killed 10 knights, including friedns, without good reason, on something of a sudden whim. Either we gerrymander LG to include this - which is silly - or we let chivalry be our ideal and drop the alignment nonsense.
Also - a monk is necessarily Lawful in D&D, and yet pursues a type of personal glory/self-realisation. So your contrast of duty vs self is already under pressure within the game system itself. As it happens, he question of individual vs society, and the proper role of the monastic pursuit of enlightenment (is it selfish?), is a real issue in Buddhist philosophy - it underlies, in part, the notion of the Bodhisattva, and a good discussion of it can be found in Ken Jones, "The Social Fact of Buddhism". You can't make what is a live question for serious practitioners of and thinkers about the doctrine go away just by slapping the "lawful" label on the monk. Either you just ignore it (as in a light superhero game), or you make it a serious focs of play, in which case the alignment labels add nothing.
Unfortunately I've never really had players that wanted to get into much more than a casual pseudo-historical mind-set. Alignments were really just a guide to me as their DM of how they intended to play. After character creation it only really mattered for the odd spell. I guess I'm fortunate that alignment has never caused any issues that I can recall.
Alignment in that sense is harmless enough, although you'll get the odd weird thing like an angel and a PC sharing some common vulnerability to a demon's attack, despite seeming pretty different in the way their moral life plays out.
But that is not how the game presents alignment - especially not classic D&D, where alignment is part of the constraints on good RPGing of one's PC, and even in contemporary D&D, which tends to assume that the PCs are all of good alignment or good-inclined (but also ready to kill at the slightest provocation!), as if that actually
meant something.