I just wanted to add this as another example of the strong heating method of lava lamp wax rejuvenation(with a slight twist):
I found a 1974 Century lava lamp(clear fluid with green wax) on craigslist for $20 and grabbed it. Once I got it home and ran it I noticed the wax was extremely chunky, full of off white clumps in the green wax. It was one of the worst cases I've personally run across to the point it really marred the appearance. So after a little research I tried the heating method. I poured out the liquid into a container for temporary safe keeping and using a double boiler set up very slowly over probably 45 minutes heated the water to boiling and held it there for about 10 minutes. Basically the standard method. What I did different is I added about a number two pencil eraser sized blob of micro-crystalline wax once the water hit boiling and let it fully melt during the ten minutes I held it at that point. My logic was that the paraffin wax had broken down, probably affecting the branching of the hydrocarbon structure. Micro-crystalline wax is highly branched so HOPEFULLY the addition of a very small amount in contrast to the total amount of paraffin would disperse and bond with the paraffin acting loosely as a framework for wax to rebuild its proper structure onto. It was only a loose hunch and I can't verify the actually chemistry of my idea empirically. But the results were fantastic! I can't prove it wasn't just the heating but I've done it before and not gotten this good a result. So hopefully this might help someone in the future with their lamps.
After(note that while it still looks abit chunky its mostly just bubbles that have since worked mostly out)