I have a tall floor lamp that needs to be left in storage (temperature and climate not controlled) that would probably average 60-85% humidity for the upcoming week. Would that damage the electrical wiring inside the lamp itself?
No.
To expand.
A really old lamp with ancient insulation left for a long time, maybe.
Anything modern for such a short time, nope.
The biggest threat are rats eating the wiring while in storage.
Only if the wiring is really old, the kind with cloth insulation.
For a week or two, nothing should go wrong. Longer term storage may cause the socket or plug prongs to begin to tarnish and corrode. This would be after months. Spray with a lightweight oil if you’re worried.
Your proposed storage conditions are almost exactly the same as an average August day in Chicago. No harm will come to the lamp in a week.