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

Here is Why You Need An Adapter

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

Pitcairn Islands

In Pitcairn Islands, outlets of type I are in use.

Type I

Lesotho

In Lesotho, outlets of type M are in use.

Type M