I could write a whole article on why people should use lattices more. in the meantime, here is a quick trick to reposition a lattice:
Create a lattice as you normally would. In the outliner, select the lattice and the baseLattice node right underneath it. (ffd1Lattice and ffd1Base for example). With these TWO nodes selected, you can translate, rotate, scale your lattice into whatever position you want. It will not deform your model when you do this. A lattice is a deformer that references the differences between it’s (hidden) baseLattice and the regular lattice cage. When you move both uniformly, they both line up exactly and therfore produce no deformations. When you are done repositioning, deselect the base and edit the lattice as usual.
Understanding this basic function of lattices will open a whole new world for you. I quite often use a base lattice parented to a lattice trick to simulate muscle sliding. It looks great and has a negligible overhead. I will hopefully post a scene file demonstrating this technique in the future.