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

Here is Why You Need An Adapter

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

Burkina Faso

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

Type C

Type E

Lesotho

In Lesotho, outlets of type M are in use.

Type M