The lich gains the following legendary action options, which replace all of the lich’s legendary actions.
This is consistent with what's written in Volo's Guide to Monsters,but it's not especially useful when using the monster's stat block. The lich can take 3 legendary actions.
The Mind Flayer Lich (Illithilich) doesn't say how many legendary actions it has. Instead, it says
This is consistent with what's written in Volo's Guide to Monsters, but it's not especially useful when using the monster's stat block. The lich can take 3 legendary actions.
Looks like a mistake in applying the variant changes, easy to fix. Hopefully a mod sees this.