You Do Need power plug adapter while traveling from Liechtenstein to Vatican City.

Here is Why You Need An Adapter

The outlet and plug type used in Vatican City are C, F and L and in Liechtenstein are C and J. This is how they look like.

Liechtenstein

In Liechtenstein, outlets of type C and J are in use.

Type C

Type J

Vatican City

In Vatican City, outlets of type C, F and L are in use.

Type C

Type F

Type L