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

Here is Why You Need An Adapter

The outlet and plug type used in Tanzania are D and G and in Lesotho is M. This is how they look like.

Lesotho

In Lesotho, outlets of type M are in use.

Type M

Tanzania

In Tanzania, outlets of type D and G are in use.

Type D

Type G