A lathe object is constructed as a surface of revolution described by a swept spline contour that you can manipulate.
You will find a Lathe in the Asset Library under Shape.
Choose Edit Shape from the Inspect Menu to manipulate the shape via circular control handles that show in blue wireframe. These move the control points for the swept spline curve. If you click on somewhere there isn't a handle, a new control point will be created there.
As well as manipulating the overall shape, you can also change how the shape is constructed from the Inspector:
Curve Smoothing
Choose between: None, Low, Medium, High. None will use straight lines between control points. Low, Medium, High will produce succesively smoother curves between control points.
Facets per Turn
Sets how many facets are used around the axis. Small numbers like 3-6 can be used for special effect. High numbers will make for smoother circles.
A shape with no curve smoothing and only 4 facets per turn (i.e., square).