Let the globe fully cool so that the lava hardens. Then pour the liquid out into another clean container. Usually the wax, though hardened, is still loose in the bottom of the globe so to prevent it from knocking around in the globe while I pour off the liquid I will hold the wax in place with a long probe that reaches the bottom of the globe.
After the liquid is poured off you can melt the wax by placing the globe in a double boiler or something else that allows the globe to be heated without subjecting the glass to direct contact to the heat source.
Let the wax fully melt and then pour it off into a clean glass jar. Now you can remove the coil and either clean it or if it is rusty replace it. Lowe's stocks a spring that is perfect for a coil.
After you have cleaned your globe and replaced the coil, the trick to pouring the wax back in without making a mess is to affix a piece of a thin hose to the end of a funnel that just reaches to the bottom of the globe. Pour your wax in and when the wax hardens pour the liquid back in. Fire it up and see if all runs well.