Morphological segmentation is an effective sparsity reduction strategy for statistical machine translation (SMT) involving morphologically complex languages. When translating into a segmented language, an extra step is required to desegment the output; previous studies have desegmented the 1-best output from the decoder. In this paper, we expand our translation options by desegmentingn-best lists or lattices. Our novel lattice desegmentation algorithm effectively combines both segmented and desegmented views of the target language for a large subspace of possible translation outputs, which allows for inclusion of features related to the desegmentation process, as well as an unsegmented language model (LM). We investigate this technique in the context of English-to-Arabic and English-to-Finnish translation, showing significant improvements in translation quality over desegmentation of 1-best decoder outputs.