Where in Night does Elie indicate that the only reason he is still alive is pure luck?

This will require you to pour through the narrative in a
rather intense manner.  I am not sure you are going to find a quote that discusses the
issue of "pure luck" as being critical to his survival.  The reason being is that the
nature of the narrative is so emotionally wrenching and so honest from an affective
point of view that the cerebral issues of luck and calculation are not as evident.  At
the same time, the implication of luck being a survival tendency implies some level of
contentment about such a predicament.  I am not really sure that Wiesel is going to take
this line of thought.  For example, he actually points out to moments where critical
decisions were made and "bad luck" followed.  The decision for he and his father to
leave the infirmary and try to run away on foot was one such instance, for the infirmary
patients were saved and liberated two days later.  You might want to expand the
discussion a bit and incorporate what it means to experience a loss of faith.  This
might not be exactly where you are going with the luck concept, but in discussing how
religious faith was withered during the Holocaust, the randomness of survival is
something that can be quite a logical move.  In this light, identifying the incident
with Moshe the Beadle, the first night Eliezer arrives in the camps and sees sights that
cause him to compose the poem, "Never Shall I Forget," as well as the hanging of the
small child could all be instances where quotations from the text could help discuss
Eliezer's repudiation of his own spiritual sense of self as being critical for his
survival.