In this paper we combine the advantages of a model using global source sentence contexts, the Discriminative Word Lexicon, and neural networks. By using deep neural networks instead of the linear maximum entropy model in the Discriminative Word Lexicon models, we are able to leverage dependencies between different source words due to the non-linearity. Furthermore, the models for different target words can share parameters and therefore data sparsity problems are effectively reduced. By using this approach in a state-of-the-art translation system, we can improve the performance by up to 0.5 BLEU points for three different language pairs on the TED translation task.