The question is not which article is correct, but which meaning the speaker has in mind and wants to convey. The choice of article is made at a really deep level and native speakers do not tend to plan it out consciously, although a careful author might very well do so.
We can indeed say
They went in search of a wagon to take the lion to a zoo.
When would we use a?
a zoo might be used if the situation was one where the trappers needed to find a zoo that would accept the lion, or if the town or city did not have its own zoo. In other words, if this story were not a parable but an account in the newspaper.
The parable presents a simpler world without such vagaries or logistical issues. They are completely out of mind.
The story, by using the, takes for granted that every town has a zoo or glosses over the fact that not every town has its own zoo because such issues are unimportant in the context of the story. The idea could be as simple as the natural place to take a lion you have trapped is the zoo, the one that always exists, of course, the place with all the animals in cages or in mock habitats.