I've always understood the term luck to indicate nothing more than having a desirable outcome despite the odds. In other words, flipping a coin and having it land heads three times in a row is an example of luck (assuming you were hoping for 3 heads). There's nothing supernatural about it, it's just that you by chance happened to get the positive result instead of a negative one.
I think you're safe sticking with luck. I think you only need to avoid referring to things like providence, saying that you are blessed, or getting caught up in any form of "law of attraction" nonsense.
Comes down to definitions. I'd say I was lucky to be born in a time and place where I had decent opportunities ahead of me and didn't have to struggle to survive. By saying 'lucky', I am only recognizing circumstances which benefited me, yet arose through no actions or merit of my own. I am not suggesting that there is some active force creating fortunate outcomes for me.
Chance has no memory, but after a series of random events we'll have a curve on which the outcomes are distributed. We'd describe someone at the far end of the curve as lucky. I don't think we should ascribe magic powers to people who have had events in the past turn out in their favor. If I rolled lots of 20s last game, I submit that I am no more likely to roll 20 the next toss (given fair dice).
Now that I am thinking about fair dice, in terms of the human condition, I don't believe people are born with the same set. I think a lot of what we're referring to as a person's luck may be better described as a person's privilege. It can come in the form of wealth, parenting, intelligence, beauty, athleticism, artistic talent or whatever. Privileged people are more likely to have what could be considered a lucky life. Outcomes more frequently fall in their favor, given equal effort.
Are you trying to get an "Intro to Philosophy?"
Let's start with - "existence"
The feeling is a result of outcome vs expectation. Dopamine, and other neuro-elements at play. It's sometimes pretty powerful, so it makes some people think the feeling's attached to something bigger than themselves, whatever that might be.