Neil Fraser was curious about this question, so he built a centrifuge at home and recorded a lava lamp at 3G (which is higher than Jupiter, actually). He explains the details here.
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It must be a lot more fun to be a mad inventor nowadays when you can show the result of your wierd experiments on youtube and get an audience 🙂
Niel should send this to the Mechano folks (since it looks like a mechano set was used. Seriously it does suggest that the density contrast in the Lava lamp is to large to work as well at 3 g as one g. Which is not surprising, given the greater forces involved. Clearly one could build a lava lamp for Jupiter, but might want to pick materials where the force difference was more equivalent to the difference in forces on the earth. This does suggest that if one went up much further in G forces the lamp would cease to work as the materials permanently stratify after the heat reaches equilibrium.