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

Here is Why You Need An Adapter

The outlet and plug type used in South Sudan are C and D and in Lesotho is M. This is how they look like.

Lesotho

In Lesotho, outlets of type M are in use.

Type M

South Sudan

In South Sudan, outlets of type C and D are in use.

Type C

Type D