Ada Lovelace is described on Wikipedia as an English mathematician and writer. That wording reflects both halves of her historical reputation: she worked deeply with mathematics and also produced influential scientific writing.
Lovelace is best known for her collaboration with Charles Babbage on the proposed Analytical Engine. In 1843, she translated Luigi Menabrea's article about the machine and added seven extensive notes of her own. One note described a method for calculating Bernoulli numbers, often called the first published computer program.
Her writing was not merely a transcription of Babbage's ideas. Lovelace explained how a general-purpose machine might manipulate symbols beyond numbers, including musical or artistic information. Her imaginative approach is sometimes summarized by her phrase “poetical science.”
The answer is not “composer,” even though she wrote about the possibility of machines handling music. Nor was she primarily a physician or sculptor. “Writer” is the exact biographical description and the fair quiz answer.