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

Here is Why You Need An Adapter

The outlet and plug type used in Djibouti 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

Djibouti

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

Type C

Type E