There should indeed be a possibility of lying. Maybe, once you are free, an option comes up that you must respond to within, say, 5 days, and you can convert or not. If you refuse, you take some H/P penalty if you earlier accepted.
So the flow would be:
1a. Judge clicks "forced conversion" without auto-torture checked
1b. Judge clicks "forced conversion" with auto-torture checked
1a.2a. Prisoner agrees to convert
1a.2b. Prisoner refused to convert, end of interaction
1a.2a.3a. Prisoner goes free; five days later prisoner has option to convert. Prisoner accepts option, and converts, end of interaction.
1a.2a.3b. Prisoner goes free; five days later prisoner has option to convert. Prisoner refuses option, suffers H/P penalty, end of interaction.
1b.2a. Prisoner agrees to convert
1b.2b. Prisoner refuses to convert, is tortured (possible second option to convert?), end of interaction
1a.2a.3a. Prisoner goes free; five days later prisoner has option to convert. Prisoner accepts option, and converts, end of interaction.
1a.2a.3b. Prisoner goes free; five days later prisoner has option to convert. Prisoner refuses option, suffers H/P penalty, end of interaction.