You Do Need power plug adapter while traveling from Luxembourg to Vatican City.

Here is Why You Need An Adapter

The outlet and plug type used in Vatican City are C, F and L and in Luxembourg are C and F. This is how they look like.

Luxembourg

In Luxembourg, outlets of type C and F are in use.

Type C

Type F

Vatican City

In Vatican City, outlets of type C, F and L are in use.

Type C

Type F

Type L