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

Here is Why You Need An Adapter

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

Solomon Islands

In Solomon Islands, outlets of type G and I are in use.

Type G

Type I

Lesotho

In Lesotho, outlets of type M are in use.

Type M