Is it legal to skateboard in a permit parking only lot with no signs that say no skateboarding?

if there's no signs, then technically yes. but if it's permit parking, it's probably more upscale and you really shouldn't skateboard there.

Added: Keep in mind that whether it makes no difference is a parking lot or somebody's front lawn - BOTH ARE PRIVATE PROPERTY. The parking lot is provided for the parking of cars and when you use it for something other than parking cars, you are mis-using it.
There are probably no signs saying that you can't pitch a tent and start a campfire either, but that doesn't maen that it is legal to do so.