I've heard all kinds of answers to this question. Some believe God allows events we label "random chance." Others believe God directs and/or uses events that only seem random from our human standpoint. Let me give you an explanation of luck anyone can believe in.
This definition comes from the "great theologian" Oprah Winfrey, who defines luck as the following equation:
Preparation + Opportunity = Luck.
I can vouch for this definition. Many of those who seem to be lucky work pretty hard at being ready for "luck" to happen. A study was done that revealed those who won various sweepstakes not only won more than most folks, they lost more as well. Why? They entered sweepstakes more often! You work hard and prepare for what you choose to do with your life, then seek the opportunity to implement your preparation.
Christians are like other folks in the world in this regard. We can prepare and seek opportunity. To others, this will look just like luck, but Christians have something SO much better than luck. When Jesus gave the Sermon on the Mount in Matthew 5, he used a word we translate as "blessed." As Christians, we have untold blessings and we live as blessed people.
So what's your definition of luck? Random Chance? Oprah's definition? Why not choose the better way — the way of blessing?
Trust your heart and soul to God. Don't yearn to be lucky, feel blessed!