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

Here is Why You Need An Adapter

The outlet and plug type used in Saint Barthélemy are C and E 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

Saint Barthélemy

In Saint Barthélemy, outlets of type C and E are in use.

Type C

Type E