Because their car broke down, preventing them from going on their way, so they had to stay at the inn.
Explanation:
Tom and Lily are characters in the "Searching for Summer" story. They just got married and decide to travel on their own to enjoy a happy honeymoon. However, in the middle of the trip, their car starts showing signs of malfunction and after a while the car stops working entirely. It is already very late and getting dark, so they decide to spend the night at the Sunrise Sun Inn in Molesworth, so that the next day they can solve the car problem.