As it happens through luck (2,6)
I believe the answer is:
by chance
'as it happens' is the definition.
'through luck' is the wordplay.
'through' becomes 'by'.
'luck' becomes 'chance' ('chance' can be a synonym of 'luck').
'by'+'chance'='BY CHANCE'
(Other definitions for by chance that I've seen before include "unwittingly" , "Without advance planning" , "As it happened, without being planned" , "Accidentally, not planned" , "Fortuitously" .)