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

Here is Why You Need An Adapter

The outlet and plug type used in Nauru is I and in Lesotho is M. This is how they look like.

Lesotho

In Lesotho, outlets of type M are in use.

Type M

Nauru

In Nauru, outlets of type I are in use.

Type I