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

Here is Why You Need An Adapter

The outlet and plug type used in Saint Lucia is G and in Dominica are D and G. This is how they look like.

Dominica

In Dominica, outlets of type D and G are in use.

Type D

Type G

Saint Lucia

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

Type G