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

Here is Why You Need An Adapter

The outlet and plug type used in Lesotho is M and in Taiwan are A and B. This is how they look like.

Taiwan

In Taiwan, outlets of type A and B are in use.

Type A

Type B

Lesotho

In Lesotho, outlets of type M are in use.

Type M