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

Here is Why You Need An Adapter

The outlet and plug type used in Burkina Faso are C and E and in Lesotho is M. This is how they look like.

Lesotho

In Lesotho, outlets of type M are in use.

Type M

Burkina Faso

In Burkina Faso, outlets of type C and E are in use.

Type C

Type E