Anything a Lathe or a Line can do in Curvy 3D 4, Curvy 3D 5 can do better - with fully customised profile shapes to add simple details to your models.
This example shows 1 curve to draw the profile, and 1 curve to shape the side of the Lathe. The same technique works for any shape of lathe with more curves too.
This is in the 5.0.08 Beta. First draw a loop shaped curve with - for example the "Create Sketch" tool. I used "Curve/Curve Symmetry" to make the loop above. Then with that object selected use "Mesh/Brush Strokes" to make a new stroke with the the loop as the 'brush'. Tick "Stretch" and "Lathe" in the Brush Strokes popup. You are now ready to draw your Lathe with one or more curves as normal, and it will use the connected brush loop to shape it.
The original loop is still editable, but you need to press 'Y' to push any changes onto your lathe.
Thank you very much for your instructions. The Brush Stroke in combination with Curve Symmetry is really next level stuff to create abstract forms ultra fast. I really love your hard work here!