You have a router / 3 axis machine (x,y,z axis) along with a rotary which we'll call A axis (4 th axis) and not a conventional lathe.
You can speak in terms of a lathe, if the rotary can be used to turn continuously other than just index and you are configuring
Mach, and also the axis which is holding the tool, such that you have an X & Z axis as conventionally defined for a lathe.
I don't know what software you are referring to. Mach is a controller which controls the axis movements based on instructions as written
or generated by specific software and how the axis are configured. There is big difference between G17 or G18 ( plane selection).
Thus you can use a lathe as a mill or a mill as a lathe, but, the software must generate appropriate code based on configuration. In general
software is specific for a lathe or mill. Mach MSN allows the user to use a mill as a lathe with mounted non-turning cutter .
2D software uses a profile. In the case of Mach Turn, it would assume that it is a conventional lathe, the profile represents a cross section
through a 3D part and thus provides a 3D symmetrical shape about the center line. A chess horse figure is not a completely symmetrical figure.
Just one example to do the horse figure you could use the mill along with the 4 axis as a rotary such that the piece is machined by rotating the axis in 2 to 4 steps and the Z axis has a rotating cutter ( say router mounted on it).
RICH