Lamp rehab

[Adam]

I am still very much in the early learning stage on lamp rehab.  I've rehabilitated a 70s century from an unfortunate encounter with a kid that decided it would look better shaken, but the white aristocrat I have pictured has a whitish dust that clouds up the water when I run the lamp and the wax has some bubbles in it.  I know from the lava library that the common prescription for cloudy water is running it for long periods of time over a month, but I want to make sure that will not make things worse in this case before I attempt it because I do not have access to a filter system or to a lot of other lamps that I can easily replace the contents.  Is it likely that running the lamp will make things worse?  thank you!