Variance is a measure of the likelihood of a range of outcomes. For example, I may have a 66% probability of a result between -$1,000 and +$1,300 over 2 hours of play. This will not change and is always the probability that my result will fall in that range.
"Luck" usually refers to a specific outcome that had a very small likelihood of occuring. Assuming I am playing the same game as above, I might say that I was "lucky" to win $20,000 over 2 hours of play (and I would be really really lucky that was the outcome, since there was only a .0002% chance of that specific outcome). Similarly, I would be "unlucky" to lose $10,000 over the same 2 hours of play.
Variance is measurable and is something you can know and plan for. Luck is unknown and is something that happens. Don't worry about luck. Focus on variance.
After all, there is a small probability that you will be hit by a falling meteor today. However, it's probably unwise to let the possibility of that "unlucky" event impact your schedule of activities.
