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

Here is Why You Need An Adapter

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

Tanzania

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

Type D

Type G

Lesotho

In Lesotho, outlets of type M are in use.

Type M