In addition to regular sentences, Joshua can decode weighted lattices encoded in the PLF format. Lattice decoding was originally added by Lane Schwartz and Chris Dyer.
Joshua will automatically detect whether the input sentence is a regular sentence (the usual case) or a lattice. If a lattice, a feature will be activated that accumulates the cost of different paths through the lattice. In this case, you need to ensure that a weight for this feature is present in your model file.
The main caveats with Joshua's PLF lattice support are that the lattice needs to be listed on a single line.