The matter is less complicated than one may think.
The following is mainly my interpretation and I might add some more text and context later.
The quote of ibn Hadi is to take in the right context which is that of the books, papers or works ibn Taymiyah compiled and it starts with his tafsir and an important part before and after this information is missing ...
The term "lying" in "Hadith terminology" comes from the following hadith:
It was narrated that ‘Ali (رضي الله عنه) said:
The Messenger of Allah (ﷺ) said: “Whoever tells a lie about me deliberately, let him take his place in Hell.”
Accordingly, The term "lying" in "Hadith terminology" refers to wrong hadith (narration/...