I doubt outside of a few exceptional cases that one is going to do better on CPU-bound problems than a well-written LAPACK implementation built for the architecture you intend to run on.
Maybe pedagogy was the point? I didn’t really get that from the article, maybe some intention was lost by filtering it through AI.
LAPACK doesn't do sparse systems.
(On the other hand, I skimmed the article and this might be a banded system, which LAPACK can handle).