Does anyone know how do you remove rusted lug nuts on a boat trailer?

That's a tough one. Usually it's impossible to get a oil into the threads. Heating works most of the time, but not always. If the wheels are aluminum, you'll usually ruin the rims. Painted wheels are going to be damaged too. You could end up breaking the lug bolts off. If they break off, oh well, they're off, just replace them. I powerful Air Impact tool will work also. Worst case is you end up breaking all of the lug bolts off. When you get the nuts off, be sure to use some "Never Seize" on the threads before installing the nuts again. That'll reduce the problem in the future.