Why do the lights turn off when I turn off the fan portion of my newly installed ceiling fan?
If the lights don't work at all, when the fan is not on: (and assuming the incoming power goes to the switches and does not come from the ceiling)

The switch for the fan, powers the switch for the lights. Instead, the incoming power at the wall switch's J-box needs a pig-tail, to feed the two switches.

Beyond that, I'd need a detailed description (preferably pictures) of the ceiling box and wall box, noting what goes where and which ones are the incoming.