I suspect the reason your Christian friend doesn't like to use words like "luck" or "lucky" is because they imply that our lives are ruled by chance. But Christians don't believe their lives are ruled by luck or chance; they believe God is in control.
Think about it: If life is random or ruled by chance, then it doesn't really have any higher purpose. In fact, if you take it to its logical conclusion it means we are here by accident, and everything that happens to us is strictly accidental and has no meaning. Or we may decide we are ruled by fate and have no control over our destiny. Like the writer of Ecclesiastes in the Old Testament, we'll be tempted to look at life and say, "All of it is meaningless, a chasing after the wind" (Ecclesiastes 2:17).
But God tells us otherwise! God created us, and He put us here for a purpose. He loves us, and He cares what happens to us! Life's greatest joy comes from discovering His purpose for our lives, and then (with His help) fulfilling it.
What is God's purpose for us? Simply this: that we would live for Him instead of for ourselves. This happens as we give our lives to Christ and learn to walk with Him every day. Don't trust "luck" to give you happiness; instead, turn to Christ and put your future into His hands.