I think that you might want to examine how Eliezer views his survival throughout the narrative. There are many moments when his faith is the divine power is questioned and doubted. This would help bring out how luck and mere chance played a role in his survival. I am not sure there is an overwhelming amount to indicate that Eliezer feels "lucky" regarding his survival. I think that there might be some aspects present that indicate his narrative involved some better aspects than others, but one does not get the feeling at the end of the book that Eliezer considers himself "lucky" for surviving. He concludes it with the suggestion that he feels that he does not even recognize the person who is staring back from a reflection of a mirror as opposed to the person he was before his struggle started.
Asking how does luck play a role in Night is asking how did luck play a roll in who survived the Holocaust. With as many people who went through "The Selection" at concentration camps every day, I think it could be argued that luck played a HUGE role. Sure there were certain criteria SS Officers were perportedly looking for as they sent men and women to the left or to the right, but how in the world could the criteria be at all fool-proof. Due to the sheer masses, either luck, fate, or faith had to have something to do with those selected to continue working vs. those selected for the gas chambers.
Consider Elie's experience in the hospital. He is advised that the Russian front is coming closer, and to get out of the hospital as quickly as possible, as everyone left would be exterminated. Elie and his father choose to leave as the decision looks like the only chance they have of survival. It turned out, the Russians arrived earlier than expected and everyone left in the hospital was spared. Lucky for those who were even sicker than Elie and could not leave.