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

Here is Why You Need An Adapter

The outlet and plug type used in Nauru is I 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

Nauru

In Nauru, outlets of type I are in use.

Type I