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

Here is Why You Need An Adapter

The outlet and plug type used in Djibouti are C and E 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

Djibouti

In Djibouti, outlets of type C and E are in use.

Type C

Type E