I've heard various conflicting explanations, and I've also heard that it varies in the different version of LAME, but what I want to know is: what exactly does the -Y switch do in LAME 3.98?

It does the same as in lame 3.97 So you can read this explanation. Very good and comprehensive.

So to sum up, if you use -V3 to -V9 then you are already getting the benefits of -Y. If you use -V2 then adding -Y just gives you the equivalent of -V3. If you use -V1 or -V0 then you apparently aren't worried about file size, so don't worry about the bits wasted by the lack of -Y. Does this sound about right?

-V2 -Y is not the same as -V3. -V2 -Y still has a bit higher bitrate than -V3, altough the bitrate bump going from -V3 -V2 is not as much when adding -Y to -V2.

What is the effect of non-integer -V values? Is there a step change in bitrate from -V2.0 to -V2.01 due to adding -Y?

-Y is on by default for -V3.000...-V9.999. There's a step between -V2.999 and -V3.

Thanks, that's pretty much exactly what I was looking for.

I was interested in this because of my iPod, which is nearly always used in conjunction with an FM adapter, and FM radio doesn't broadcast frequencies above 15 or 16 kHz anyway. But now that I have a deeper technical understanding of what's going on, I don't think any further switches will be necessary. I'm using -V 4 which has -Y enabled already. In addition, it seems like setting a lowpass would be a better way to go about cutting off these high frequencies.

Yes, because -Y is not a lowpass filter.