You Do Need power plug adapter while traveling from Saint Lucia to British Virgin Islands.

Here is Why You Need An Adapter

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

Saint Lucia

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

Type G

British Virgin Islands

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

Type A

Type B