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

Here is Why You Need An Adapter

The outlet and plug type used in Peru are A, B and C and in Liechtenstein are C and J. This is how they look like.

Liechtenstein

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

Type C

Type J

Peru

In Peru, outlets of type A, B and C are in use.

Type A

Type B

Type C