Leslie, as a general rule, tile would not go under the lip of a garden tub, but butt up to it. The lip should actually be sitting on solid support, as it does carry some weight as bathers get in & out, sit on the edge, etc. If it's a fiberglass tub, the tile could go under the edge, but I would not do so on a cast iron tub; when the tub is filled, the weight change will be enough to put some pressure on the edge, and this could break tile.
If the top edge of the tub is flat & wide enough to lap tile over the edge, you can build up around the tub & tile over the lip if you so desire.
Leslie, beyond there, it's really a matter of choice, and how the lip of the tub was designed; some will be made to work for one or both methods.