To make the lid fit on reliably with as tight as possible, the only difference you need in the box and lid dimensions is the resolution of the 3-D printer. You need to account for manufacturing inaccuracies and inconsistencies. Rapid prototyping is very reliable and not subject to the same issues as machining like tool wear and fixturing issues, but no part will ever be 100% to the design. This sort of information should be available from whoever is printing the parts for you.
You don't want a full perimeter interference fit, as the corners of the box will be pretty stiff and won't compress easily, and a full perimeter interference isn't necessary to lock it on.
However, you should look at some method of securing the lid besides it being a snug fit. There are a couple simple ways to do this, especially when 3-D printing the parts. Some kind of snap fit will prevent you from adding extra parts to the design, but will add extra stress to the printed parts. This shouldn't be a big deal, because you don't need a lot of interference, but you may want to give yourself some extra strength and bump up to 1/4" thick walls.
Another possibility is adding holes to the corners of the case to allow the lid to be screwed on. If you make the holes about the size of the shank of the screw, they should automatically thread the hole, and you won't need to tighten it too much to keep the top closed if it's just sitting on your desk.
If you want to get even more complex, you could probably even make a hinged top, buy a standard door hinge at your nearest hardware store, and use a snap fit on the other side to lock it down.
Play around with some of these ideas in Inventor and see what looks good. 3-D printing is a powerful tool that allows you to create some complex geometry, and while a couple of rectangles is really easy, if you experiment with the CAD software to see what you can design, the 3-D printer can probably do a lot of that stuff without much extra effort.