In Elvish, a Half Lich meant 'Half cultivated and not to completion'. Basically, Anglish hadn't truly transformed into the Lich yet. Despite the fact that he didn't have the full power of the Lich, Anglish also didn't have any defects.
The Half Lich were similar to the Lich; the abilities of their past life remained, and they also had limitless time to delve into studying magic. So, achieving great magic power even as a Half Lich was inevitable.
The key difference was that they couldn't place their soul into a phylactery like the Lich could. The Lich only needed a phylactery to resurrect with a new physical body. It was precisely because of this reason that the Half Lich Anglish cared about his life even more. Whenever he encountered a dangerous situation, he would more likely utilise his full power.
