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

Here is Why You Need An Adapter

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

Lesotho

In Lesotho, outlets of type M are in use.

Type M

Palestine

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

Type C

Type H