Unless your lathe has a Y axis, it should default to G18 on start up. However, most programmers worth there salt have a Safety Line at the beginning of the program to ensure that the machine control is initialized to the modes that keeps it safe and so that no alarms are raised.
I don't generally like using tool nose compensation with a Turning Centre. Its use is very necessary with a Machining Centre, to be able to adjust the size of features when using end mills and the like. However, in most cases, component size with a lathe is adjusted with the Tool Offsets and not Tool Nose Radius Offsets. Having said that, the following program snippet has used Tool Nose Radius Compensation, as I'm unaware of the tool nose radius you intend to use.
The radius of the arc that will satisfy your criteria for the convex form is 11.2624
G00 X1.580 Z0.200
G41 G01 Z-0.028
G02 X0.000 Z0.000 I-0.790 K-11.235
G40 G01 Z0.200