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

Here is Why You Need An Adapter

The outlet and plug type used in Libya are C and L 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

Libya

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

Type C

Type L