By far your best option would be to have a battery-powered unit. I haven't heard of any customer-accessible outlets in the lavatories @dfwskier but perhaps it is like riding the CTA, if you know where to look there might be one. Prevention is probably the best option - let the FA know your issue when boarding so that they can help you be re-seated if necessary. Then having your own power will be the next line of defense. Maybe third, if you find yourself in the gate area with a bunch of pets ask to be re-accomodated on a later flight. Certain routes and/or times are more likely as well - I know that I can go many trips without seeing any, but then a flight will have several. I've only ever heard of outlets in the galley areas.
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