https://www.gemsociety.org/article/lab-grown-diamonds-faq:
“Many lab-made diamonds have an inscription that identifies them as lab-made.
Diamonds can also have a lab report number inscribed on the girdle”
I think it’s very likely that, If that “above a certain carat” were true, that page would have mentioned it.
I also cannot think of a good argument why it would be reasonable to require producers of artificial diamonds to add such markers.
> I think it's mandatory that every lab-grown diamond above a certain carat are laser-engraved
That’s not “diamonds that are lab-grown by GEM Society members”.
Why would it be reasonable to require anybody who’s not the GEM Society to engrave their products, so that the GEM Society can protect its source of revenues?
But there’s also a lot of concern about stolen jewelry and even diamond swapping for seemingly legitimate businesses. So, not too hard to make it also sound like it’s for the consumers best interest.
> Diamonds are effectively worthless the moment they leave the store
That's not the case! You can have the stone removed from the ring and, in case you don't have the original certificate, sent to a certification authority (like GIA) to have it graded. I think it also, once graded, gets automatically laser-engraved (above a certain carat) but I'm not sure about that: maybe you need to pay for the laser engraving too. And it's then got a value on the market: there's a worldwide market (or several) and every single jeweler in the world can see which stones are available at which price depending on their specs and book any stone and have it shipped in a few clicks.
Source: I've got a good friend who's a jeweler and he showed that to me.
Now: fancy shops (with famous names) may make fun of people by selling them stones at 3x their values or more (I don't doubt that) but you can also go to an independent jeweler and have him model/build the ring (or he'll outsource the 3D modelling) then put the stone on it and you'll pay a price much closer to actual price of the stone (the jeweler doesn't really work harder for a 0.5 carat stone vs a 2 carat one, so the bigger the stone, the less is "wasted" on the ring).
Regarding the differing values: I think it's mandatory that every lab-grown diamond above a certain carat are laser-engraved so unless labs growing these diamonds are cheating, it's extremely hard to make a lab-grown one pass for a billion years old one.