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

Here is Why You Need An Adapter

The outlet and plug type used in Lebanon are C, 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

Lebanon

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

Type C

Type D

Type G