Final answer:
Harry first saw Remus Lupin on the Hogwarts Express in 'Harry Potter and the Prisoner of Azkaban', when Lupin was asleep in their train compartment.
Step-by-step explanation:
Harry first set eyes on Professor Lupin during an event in the Harry Potter series. The correct answer to when Harry first saw Lupin is A) On the Hogwarts Express. In 'Harry Potter and the Prisoner of Azkaban', the third book of the series, Harry, along with his friends, meets Remus Lupin when he is asleep in their compartment on the Hogwarts Express. Later, it is revealed that he is the new Defense Against the Dark Arts teacher at Hogwarts.