Why was he a sexual writer?
Complex writers can be seen as fitting many labels. D. H. Lawrence is one such writer. While he can be considered a "sexual" writer, I would submit that he is much more than solely this.
Lawrence can be considered a "sexual" writer because, frankly, he wrote about sex. Lawrence's work addressed sensual love. In works such as Lady Chatterley's Lover, The Man Who Died, Women in Love, Lawrence explores sexual dimensions within human consciousness. In his own life, Lawrence experienced the complexities of love and sex in multiple failed relationships. This played a significant role in his writing.
At the same time, Lawrence felt compelled to delve into topics like sex from an aesthetic point of view. Simply put, Lawrence believed that the artist should be able to explore any topic he or she wishes. The artist should not be limited by social conventions. It is for this reason that his work was considered "obscene" and subject to much in way of censorship. His reputation is the result of this labeling.
Lawrence is a complex thinker. He truly believed that human emotions is a critical aspect of identity. Sexual activity and exploration was a part of this primal condition. He wanted to analyze what elements made us human. Lawrence recognized that sexual drive was a part of this definition. It is for this reason that he insisted on illuminating it in such detail within his work. For this reason, he becomes labeled as a "sexual writer." In reality, he was much more.