Space-delimited words in Turkish and Hebrew text can be further segmented into meaningful units, but syntactic and semantic context is necessary to predict segmentation. At the same time, predicting correct syntactic structures relies on correct segmentation. We present a graph-based lattice dependency parser that operates on morphological lattices to represent different segmentations and morphological analyses for a given input sentence. The lattice parser predicts a dependency tree over a path in the lattice and thus solves the joint task of segmentation, morphological analysis, and syntactic parsing. We conduct experiments on the Turkish and the Hebrew treebank and show that the joint model outperforms three state-of-the-art pipeline systems on both data sets. Our work corroborates findings from constituency lattice parsing for Hebrew and presents the first results for full lattice parsing on Turkish.