ഭാഗ്യം is the usual word for good luck.
It is an "obviously Sanskrit" word. However, in Sanskrit it means "fortune", without any specific positive connotation. To specify good luck, one would say സൌഭാഗ്യം and to specify bad luck, one would say ദൌര്ഭാഗ്യം. These words mean the same in mallu as well.
ഭാഗ്യം in turn comes from ഭഗം. A little online root analysis indicates that ഭഗം = ഭ + ഗം. In Sanskrit, ഭ (among other things) means "star" (e.g. ഭചക്റം - the starry host); ഗം means "to go". So ഭഗം is the way a star goes, that is to say, decided by the stars. ഭഗ also means god (cf. ഭഗവാന്)
Now what is the pure mallu word for luck?
The Tamil word for luck is അതിര്ടം or അതിര്ഷ്ടം - definitely not "pure mallu". തലയിലെഴുത്തു് is pure mallu, but it is not exactly luck; it is fate.