You Do Need power plug adapter while traveling from Cocos (Keeling) Islands to Saint Lucia.

Here is Why You Need An Adapter

The outlet and plug type used in Saint Lucia is G and in Cocos (Keeling) Islands is I. This is how they look like.

Cocos (Keeling) Islands

In Cocos (Keeling) Islands, outlets of type I are in use.

Type I

Saint Lucia

In Saint Lucia, outlets of type G are in use.

Type G