Daggerfall Workshop Forums

Quest: Lich's Soul quest

I've killed a zombie and read short message from King of Worms, which started the quest.
But there are no any notes about the quest in quest log, no note in inventory.
After some time I had to read wiki to recall about the quest and where to go.

Is it intended that some important quests have no reminder in quest log?

That's what the wiki shows. You're expected to remember that the zombie arrived, and from then on the KOW can offer it to you. When he does, then you get a journal entry.