they actually mean 2 different things.
network actually just means things are linked together e.g. social network, internet is a network as well i.e. computers linked together. There is no such think AFAIk as a network form, its just links not structure.
lattice is a structure, just google search for an image to see what it looks like. easier than trying to explain it.
So what do they have to do with each other?
well like I say a network is linked items and a lattice is a pattern that can be used to link items. So there are things called lattice networks, but they are technical terms and not really in common use outside of the fields that use them. If you give more context I may be able to help with the specific instance you are dealing with.