According to the SQLite project homepage, all their source code is released to the "Public Domain". In other words, their source code has no copyright of any kind.
Of course this is a problematic "license" in many jurisdictions, mainly because "Public Domain" is not a legal license at all (because licenses are always based on copyright). In other words, there are many jurisdictions where copyright is automatically granted to the author and releasing something without copyright is not recognized by the laws of the jurisdiction as a valid form of publication.
Usually what this means in these jurisdictions is that if the author has not specified any legally-binding usage license for their work ("public domain" not being such), the work is simply copyrighted, period, and nobody can use it without breaking the copyright (and thus, theoretically, the author could sue for copyright infringement).
This problem would be easily solved by specifying a legally-binding usage license based on copyright. If the authors want to give complete freedom on the usage of their software, they can simply use a license which grants such freedom, such as for example the MIT License. The whole point of such a license is that they explicitly claim copyright and grant permission to use the software in any way the user wants. This is legally binding in the majority (if not all) jurisdictions which acknowledge international copyright.
Once again: Claiming no copyright is a problematic form of "licensing" because many jurisdictions don't acknowledge such a thing.
The people at the SQLite project understand this problem. Some companies in some countries may be unable to use SQLite because "public domain" is not a valid usage license in their countries. So what does the SQLite project offer for people in these jurisdictions? Maybe release the softare using a liberal licences such as the MIT license?
No, they offer to sell a license to these unfortunate people at the meager price of 1000 dollars.
Wait! What?
Yes, you read that correctly. This open source project which offers their software completely and absolutely free, to be used by anyone in any possible way the user might want to use it... sells usage licenses at 1000 dollars apiece to those unfortunate enough to live in a country which doesn't acknowledge public domain as a valid license.
They could simply publish their software under a legally-binding free software license which imposes no limitations, but no. Instead, they offer to sell a license at 1000 dollars. And if you are unfortunate enough to live in a country where "public domain" is not a legal license, you'll have to pay them that money if you want to use the software legally. They won't offer you an actual free license.
I really can't understand what's the big idea. Is this some kind of indirect revenge against countries which do not recognize "public domain" as a valid usage license? By punishing the people living in those countries? If your country recognizes "public domain" as a valid license, then you are completely free to use our software in any way you like, but if your country doesn't recognize it, then the price is 1000 dollars, thank you very much.
(Of course as an individual you could "pirate" SQLite without consequences because the project isn't going to sue you. However, a company might not have that kind of luxury, depending on how by-the-book they go with the legality of their actions. However, technically speaking you are infringing copyright even as an individual, even if you don't get sued. All this could be easily solved if the project would simply offer you a free license. But they don't.)
Oh, and SQLite is not the only open source project doing this. Pro tip: If you ever write to the Free Software Foundation asking about their usage licenses (GPL, LGPL...), don't mention that you are working for a company writing proprietary software. If you do, they won't answer your questions unless you pay them 150 dollars.
Yeah. That's "free" software for you.