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

Here is Why You Need An Adapter

The outlet and plug type used in South Africa are C, M and N and in Lesotho is M. This is how they look like.

Lesotho

In Lesotho, outlets of type M are in use.

Type M

South Africa

In South Africa, outlets of type C, M and N are in use.

Type C

Type M

Type N