The present work proposes the use of Latent Dirichlet Allocation to model Extraordinary Appeals received by Brazil’s Supreme Court. The data consist of a corpus of 45,532 lawsuits manually annotated by the Court’s experts with theme labels, a multi-class and multi-label classification task. We initially train models with 10 and 30 topics and analyze their semantics by examining each topic’s most relevant words and their most representative texts, aiming to evaluate model interpretability and quality. We also train models with 30, 100, 300 and 1,000 topics, and quantitatively evaluate their potential using the topics to generate feature vectors for each appeal. These vectors are then used to train a lawsuit theme classifier. We compare traditional bag-of-words approaches (word counts and tf-idf values) with the topic-based text representation to assess topic relevancy. Our topics semantic analysis demonstrate that our models with 10 and 30 topics were capable of capturing some of the legal matters discussed by the Court. In addition, our experiments show that the model with 300 topics was the best text vectoriser and that the interpretable, low dimensional representations it generates achieve good classification results.