Even easier than the Scale tool for this is the Tape Measure tool. If, in the case of the cube, you know you want it to be 75", measure from one corner to the other making sure to click on it both corners. Then type 75 and hit Enter. If you only want to resize the group or component in question, open it for editing, first.
To the OP, in the case of resizing the lattice, is it all dimensions that need to be changed or just the overall size? It sounds to me as if the slats are probably the correct size and you only want to change the outside dimensions. In the case, scaling is absolutely the wrong tool to use. Instead, it sounds like you need to cut the lattice down to size. In the case you can draw a cutting plane at the correct location and use it to trim the slats. Without seeing the lattice model it's difficult to give more instructions but one consideration, depending on how the lattice is designed is that you may want to trim away some on both sides to keep things centered.
