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

Here is Why You Need An Adapter

The outlet and plug type used in Lesotho is M and in Palestine are C and H. This is how they look like.

Palestine

In Palestine, outlets of type C and H are in use.

Type C

Type H

Lesotho

In Lesotho, outlets of type M are in use.

Type M