It depends.
My favorite
answer would be "never". Most folks that aerate get very little gain from it. If you need aeration, that could be a sign that your soil sucks and you
should look into that. Maybe aeration can be part of far larger plan to improve the soil - but most aeration is not that.
I wonder if aeration is used by chem lawns because there are no longer earthworms to do the job.
I suspect that a
lawn that is loaded to the gills with earthworms has no need for aeration.
All that being said: if I had miserable, wormless dirt and I was bringing in a load of
compost and lime in the spring or fall, I think it would help to aerate just before that.
BUT! Let me be even a little more obnoxious about this: I, personally, would never aerate my own lawn. If it was so horrible that what the soil needed was to aerate, then I would either till, or I would plant a cover crop to rip open the soil and introduce a whole bunch of organic matter.