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

Here is Why You Need An Adapter

The outlet and plug type used in Lesotho is M and in New Caledonia are C and F. This is how they look like.

New Caledonia

In New Caledonia, outlets of type C and F are in use.

Type C

Type F

Lesotho

In Lesotho, outlets of type M are in use.

Type M