Great question. The short answer is that the development of faeries being literally unable to lie is a more modern take1. There's no question faeries could be deceptive in earlier traditions, but outright lying is atypical. Additionally, your question raises interesting related points about the relevant folklore.
Insofar as faeries and lying goes, there's nuance here between earlier traditions2 and more recent portrayals: Generally speaking, older stories feature faeries who will not lie rather than explicitly indicating they cannot lie.
The distinction here is an important one: if you're fundamentally unable to lie, then you never have to choose whether to be truthful. You might wish you could lie about something and regret not being able to.
(Why is this important? Folk-tales overall tend to portray the world as a place where there is a proper, natural order to things. We pass down folk-tales partly to explain either how things "are" or how we feel the world ideally "should be.")
In your example about the Welsh boy, the faeries "don't make oaths," not because it's impossible for them to lie and thus pointless to do so, but because they abhor lying, so it's completely unnecessary. By extension, this reflects the notion that, although human beings are perfectly capable of telling lies, a person should likewise find breaking their word "unnatural," so to speak. (This is not to imply that faeries themselves are normally meant to serve as models of human behavior.)
More to your question, consider how faerie mythology commonly features the notion of faeries being tricksters or manipulative. Oftentimes, the way you overcome some faerie mischief is by outsmarting the faerie or discovering an important secret about them -- beating them at their own game. If faeries didn't abide by their codes, there would be no order and you would never "win." (The tale with Rumpelstiltskin would be less compelling if at the end he yelled "Psych!" and made off with the goods, anyway.)
Now, when I say “code,” I don’t necessarily mean “code of honor": while faeries are often helpful and friendly, then can just as soon be very much the opposite of honorable and helpful by our typical human ideals. It’s more about adherence to a set of personal or societal standards, though what exactly such “standards” might be for a faerie varies depending on the tale. The point is that faeries play by their own rules, but they do stick to those rules, by and large.
To sum-up, the concept of lying in itself is not really an overt concern in most western folk-tales where supernatural beings are up to perfidious deeds3. Any verbal trickery more often entails misleading or ambiguous wording rather than outright lies. Returning to the tale you mentioned, I find it interesting that the recorded versions we have of it today make mention of these faeries' love of truth, as this seems to have no real bearing on the story. Perhaps we're missing a piece now, or two versions were conflated wherein the faeries served as an example to the boy: in a related form of this tale, it isn't theft that crosses the faeries, but the fact the boy had agreed not to reveal their existence whatsoever and subsequently breaks his word. Other versions combine this with another common motif: he's allowed to take gold back with him on the promise of not revealing the source of the gold, yet he ultimately does. (In the boy's defense, it's usually because his suspicious father beats it out of him. Perhaps one take-away should be that he could have lied to his father, but didn’t?)
As for other forms of deceitful actions, there are, of course, changelings, which you bring up in comments. There are also tales regarding faeries in markets paying with fake money that later reverts to some worthless thing, or even simply stealing outright.
For further reading, I will refer you to two sources. Both of these collections were compiled over 100 years ago when much of this knowledge remained much more fresh than it is today. (Be warned, however, that these books are long, wordy, and in the second instance, intentionally redundant for the sake of thoroughness.) You should find that overwhelmingly faerie mythology is more about mischief and trickery without ever really saying they are unable to lie:
There is a version of Thomas Keightley's "The Fairy Mythology" on Project Gutenberg, published 1892. (It also contains a version of the Elidurus tale with similar wording to the one you quoted.)
Google Play Books has multiple versions (some free) of John Rhys' "Celtic Folklore: Welsh and Manx," first published in 1901 in two volumes.
If you want to do a real deep-dive into "Celtic" lore in general, I would start with Rhys. He basically piled together everything he could find, giving multiple iterations of the same tales/themes (and often in the words of a source directly) to highlight similarities and differences. As such, it's repetitive, but robust.
1 It's always worth mentioning that contemporary ideas about faeries are heavily influenced by Tolkien's impactful portrayal of his noble (faerie-inspired) elven race. His fingerprints are all over the modern fantasy genre.
2 The British Isles, France, and the Iberian Peninsula are the regions I'm mostly knowledgeable of, and this is the position I am answering from. But I can tell you there are certainly some similarities between these areas and Germanic and Eastern European folk-tales. Likewise, Scandinavian folklore shares thematic commonalities with English and other Western European lore due to cultural interactions and common sources, while also having their own brands of mythological creatures. Perhaps others can chime in with information about these other regions' traditions.
3 You will also find this motif extended to other supernatural beings within the same regional folk traditions, notably Satan and witches.
