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

Here is Why You Need An Adapter

The outlet and plug type used in Canary Islands are C, E and F 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

Canary Islands

In Canary Islands, outlets of type C, E and F are in use.

Type C

Type E

Type F