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

Here is Why You Need An Adapter

The outlet and plug type used in Luxembourg are C and F and in Lesotho is M. This is how they look like.

Lesotho

In Lesotho, outlets of type M are in use.

Type M

Luxembourg

In Luxembourg, outlets of type C and F are in use.

Type C

Type F