il mango's short video about stone generators.
Basically, random ticks can force lava to move.
I saw that video when it was released, but they're ultimately problematic designs. They don't self-repair, and they break if you aren't actively removing the stone.
I built an updated version in the vault at spawn that I think works better on a multiplayer server, but it could still break if it ran autonomously and stone wasn't actively removed. So instead it only gives you more stone if you removed the existing stone which solves this problem.
That said, personally I still prefer self-repairing designs that don't require observer blocks. Essentially the piston that feeds the stone out of the machine also clears the water and lava flows so that they can reset easily and quickly in the case of lava flowing faster than water in some cases.
Here are some pictures of that design, built in a way so you can see how it works, but I have built a more compact version of the rear mechanism that is just a bit harder to see what is going on.
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I use this device on skyblock becuase it's fast, easy to build, efficient, and self-repairing. Even if you just want cobblestone, smooth stone is faster to mine into cobblestone.
The lever is just to turn the machine on and off so you don't leave it running, but you could also easily use a pressure plate instead placed where you would stand while mining.
Off-topic: Someone had fun decorating the Spawn basement. xD What happened to snowman faces though? 
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Heh, that was me. You use shears to remove the pumpkin heads.