How could I write an essay about The Song of the Lark?

There are different critical essays you could write on The Song of the Lark. One theme running throughout the book is the sacrifices that Thea makes for her art (which turns out to be singing). She must, over time, repudiate the demands of her family and upbringing to become a truly great artist.

Even while living in Moonstone (in Colorado), she shows independence of spirit by befriending people like Professor Wunsch and Spanish Johnny,...

There are different critical essays you could write on The Song of the Lark. One theme running throughout the book is the sacrifices that Thea makes for her art (which turns out to be singing). She must, over time, repudiate the demands of her family and upbringing to become a truly great artist.

Even while living in Moonstone (in Colorado), she shows independence of spirit by befriending people like Professor Wunsch and Spanish Johnny, who are both culturally and morally at odds with people in the town. Later, when Thea dedicates herself to singing, she leaves Moonstone and cannot return even to attend her mother's funeral. As an opera singer, she dedicates herself fully to her career and does not have time at the height of her career for a family. The novel speaks about what it means to be an artist, and Cather suggests that artists are freethinkers who are willing to separate themselves from what they know and the life they are born into. One of the themes you could write about, then, is the life of an artist. 

You could also focus on the mentors who help Thea become a great artist, including Dr. Archie and Frederick Ottenburg. What is Cather suggesting about an artist's need for understanding and mentorship to develop his or her art? These two men are critical to Thea, and their support is vital in helping her flourish.