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This paper describes the NYU submission to the CoNLL-SIGMORPHON 2018 shared task on universal morphological reinflection. Our system participates in the low-resource setting of Task 2, track 2, i.e., it predicts morphologically inflected forms in context: given a lemma and a context sentence, it produces a form of the lemma which might be used at an indicated position in the sentence. It is based on the standard attention-based LSTM encoder-decoder model, but makes use of multiple encoders to process all parts of the context as well as the lemma. In the official shared task evaluation, our system obtains the second best results out of 5 submissions for the competition it entered and strongly outperforms the official baseline.