Honestly i don't believe in the concept of luck, in my opinion it's all decided by chance and the more your karma is positive the more you have hopes of making it, in my spiritual opinion. There is no person who is luckier than others, i would say more that there are people who are more deserving that karma makes them happy
That's just putting other superstition (karma) over other(lucky).
The fact that luck is decided by change is what luck means like you said, but you can use the word in secular way, to describe past events of someone who has been lucky, without mystifying it as some predictable concept. It's not a matter of belief
Karma on the other hand can't really be used other then mystified / spiritual sense. That's a matter of belief.