We propose a neural network model to estimate word translation probabilities for Cross-Lingual Information Retrieval (CLIR). The model estimates better probabilities for word translations than automatic word alignments alone, and generalizes to unseen source-target word pairs. We further improve the lexical neural translation model (and subsequently CLIR), by incorporating source word context, and by encoding the character sequences of input source words to generate translations of out-of-vocabulary words. To be effective, neural network models typically need training on large amounts of data labeled directly on the final task, in this case relevance to queries. In contrast, our approach only requires parallel data to train the translation model, and uses an unsupervised model to compute CLIR relevance scores.