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

Here is Why You Need An Adapter

The outlet and plug type used in Kiribati is I 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

Kiribati

In Kiribati, outlets of type I are in use.

Type I