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

Here is Why You Need An Adapter

The outlet and plug type used in Liechtenstein are C and J 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

Liechtenstein

In Liechtenstein, outlets of type C and J are in use.

Type C

Type J