Well; I read the blog post and I am disappointed at Lemire, actually.

Yes, it does not claim anywhere it is his invention - it starts the description of the algorithm with "The common solution", but if you read it, it really looks like the development of the technique as a whole is his; at the end one note says: "The technique described in this blog post is in used within Microsoft Arriba."

If no one had pointed out that it is not his, I would have thought that it was his, the blog post title is "A fast alternative to the fast modulo reduction", and not "How X's algorithm for fast modulo reduction works. My implementation".

That's a fair point. Generally I am used to seeing a cite of original source on an elaboration, proof, or "let's dig into how it works" sort of writeups on algorithmic approaches. (Sometimes this is done even when the algorithm in question and source is well known.) Specially if the author is an academic.