When taking the contents out of a lamp and putting them back in there is a risk that the wax will start to stick to the globe if the globe is not cleaned properly. With the bottle empty, use Dawn dish soap and lots of shaking, refilling and dumping is usually enough to clean out a lamp. It also helps to put a paper towel in the bottle while doing this. You might also find some sort of stick and attach a brush or sponge to wipe the sides down as well. I have used a wooden skewer with a Magic Eraser rubber-banded to it to swipe down the inside of the lamp with great success.
When putting the contents back in, some have had success by coating the globe with a surfactant (bubble soap, dish soap, GooKit surf) first, swishing it around and then pouring it out, leaving a thin coating behind.This coating can help the wax not stick to the sides of the globe.
Sometimes this is not enough. If the lamp has been ran for too long and the wax has been burnt up, you may need to take an extra step. Since wax is a petroleum product, gasoline and paint thinner work very well to dissolve the wax. Gasoline works better than paint thinner, but it may scare you off due to how flammable it is. Gasoline used to be used as an all purpose cleaner a while back (ask your grandparents/parents), so it is not that uncommon! You will need to let the lamp soak for 24 hours to make sure the hardest, crustiest, burnt-on wax is dissolved. Otherwise when you refill the bottle the wax will stick again! The wax may still stick to the globe after trying all of these methods. Nobody has yet to find a method that works every time 100% of the time. If you know how to fix sticking wax post your solution!
If your lamp started sticking on its own, it may not be possible to fix it. Most USA lamps can be fixed by following the above steps, but Chinese-made lamps can have bad formula and will stick no matter what.