Random fluctuations and butterfly effects aside, couldn’t you actually predict the lava lamp flows from fluid dynamics? Or does it just so happen that the math here is actually harder than breaking the encryption?
But that's one whopping reservation, and even if, you could only predict exactly to the extent fluid dynamics exactly models interacting particle physics involving mind-boggling numbers (for the scales of interest).
Also, I have no background solving complex fluid dynamics problems, but my understanding is that the differential equations involved generally have to be solved with iterated numerical approximations (if anyone here knows more certainly, please do chime in). In the short term that's probably one of the smaller problems, but it is at least somewhat connected to why we don't get get highly reliable 3-week weather forecasts, and possibly never will.