Here, moving from left to right or bottom of the piece to the top, I have used a bead to a fillet, a small cove to another fillet, a larger cove and a bead for the shaft to rest on. For the most part I have not measured per se, just have gone with what looked right.
Position the tool rest at the face of the piece.
Turn a mortice for the tenon of the shaft to fit later. Ensure that the sides of the tenon are straight, that is, they should neither angle in nor out. It could be drilled on the lathe but for a simple mortice such as this, it is faster to use a scraper or similar tool. No measurement here is critical except to later turn the tenon to fit the mortice.
Now a short pause. It is necessary to drill a hole along the center line of the base to intersect another hole whilch will be drilled down the center of the shaft so as to fit the lamp cord. If you have a set up for this great, else take a square of hard wood at least four inches longer than the swing of your lathe and turn a two inch tenon the size of your tool rest post.
Put the square in the tool rest and secure it. Bring up the tail center and tap it into the square to mark the exact lenter line. Off the lathe drill a 5/16' hole through the square.
Place the new drill jig in line with the bottom of the base at least a quarter inch from the bottom and angled toward the top about 2°. Using the jig as a guide, drill the hole most of the way to center. Remember there is a screw in the way right at center. The hole can be finished up when the base is removed.