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

Here is Why You Need An Adapter

The outlet and plug type used in Dominica are D and G and in Libya are C and L. This is how they look like.

Libya

In Libya, outlets of type C and L are in use.

Type C

Type L

Dominica

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

Type D

Type G