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

Here is Why You Need An Adapter

The outlet and plug type used in Solomon Islands are G and I 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

Solomon Islands

In Solomon Islands, outlets of type G and I are in use.

Type G

Type I