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

Here is Why You Need An Adapter

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

Lesotho

In Lesotho, outlets of type M are in use.

Type M

Cayman Islands

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

Type A

Type B