Rod,
While the user interface Axis "knows" it is in lathe mode EMC has no such thing as lathe mode and defaults to G17 XY plane when started. While you can put G18 in your ini file that won't stop another g code program from changing it so it is always best practice to put all your setup g codes in the preamble of your program. I include a standard line similar to G7 G18 G20... as the first line of all my g code files.
Even though you only have two axis on a lathe they are 0 and 2 so you need to load 3.
I'd bet your offsets are not correct as that it the hardest thing to get right.
Just drawing your arc in ACAD and I have the following coordinates.
Arc Start X27.535 Z0
Arc Center X31.250 Z-11.1999
Arc End X19.450 Z-11.200
Doing the math I get
X offset 3.715
Z offset -11.1999
So I end up with:
G8 G18 G21
G0 X27.535 Z0
G3 X19.45 Z-11.2 I3.715 K-11.200
This give me an arc of about 270 degrees... not sure your wanting that. Changing to G2 give me about 90 degrees.
Scrolling down to compare I this I see your using the XY offsets IJ instead of the XZ offsets of IK... so your math was sound.
www.linuxcnc.org/docview/html//gcode_main.html#sub:G2,-G3:-Arc
John