You Do Need power plug adapter while traveling from Palau to Saint Lucia.

Here is Why You Need An Adapter

The outlet and plug type used in Saint Lucia is G and in Palau are A and B. This is how they look like.

Palau

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

Type A

Type B

Saint Lucia

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

Type G