Connect Segments: When checked, the tool will create polygons "joining" each level or segment in the lathe, creating a traditional ducted solid.
Create Endcap: When checked, the tool will create an "endcap" polygon at the far extent of the lathe, identical to the polygons being lathed.
Create Layers: When checked, the tool will create "layer" polygons at each segment in the lathe, identical to the polygons(s) being lathed. Normally, this option would be used with Connect Segments off, to create clones of the selected polygons.
Lathe Last: When checked, with Connect Segments on, the tool will lathe the last segment of each selected polygon.
Delete Interior:
Segments: Controls the number of segments, or "layers" in the lathe.
Rotate X, Y, Z: Control how far the lathe is offset along the axes. Use the ControlChannels to make the offsets non-linear along each axis.
Offsets X, Y, Z: Control how far the lathe is offset along the axes. Use the ControlChannels to make the offsets non-linear along each axis.
Scale X, Y, Z: Control the scaling of the lathe polygons along each axis. Use the ControlChannels to make the scale factors non-linear along each axis.
OK: Creates the lathe polygons and closes the tool.
Cancel: Closes the tool without creating the lathe polygons.
The Lathe tool also includes a standard Origin Tab, allowing you to set the Origin around which the tool lathes polygons.