Abstract Lattices are an efficient and effective method to encode ambiguity of upstream systems in natural language processing tasks, for example to compactly capture multiple speech recognition hypotheses, or to represent multiple linguistic analyses. Previous work has extended recurrent neural networks to model lattice inputs and achieved improvements in various tasks, but these models suffer from very slow computation speeds. This paper extends the recently proposed paradigm of self-attention to handle lattice inputs. Self-attention is a sequence modeling technique that relates inputs to one another by computing pairwise similarities and has gained popularity for both its strong results and its computational efficiency. To extend such models to handle lattices, we introduce probabilistic reachability masks that incorporate lattice structure into the model and support lattice scores if available. We also propose a method for adapting positional embeddings to lattice structures. We apply the proposed model to a speech translation task and find that it outperforms all examined baselines while being much faster to compute than previous neural lattice models during both training and inference.