You Do Need power plug adapter while traveling from Luxembourg to Isle of Man.

Here is Why You Need An Adapter

The outlet and plug type used in Isle of Man are C and G 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

Isle of Man

In Isle of Man, outlets of type C and G are in use.

Type C

Type G