How to remove large amounts of lava in Minecraft?

The quickest way is to just pour in water( source block outside of lava) when the water hits the lava it turns into obsidian. Then you can mine it up or leave it.

Dump a bucket of water nearby (not directly on the lava or it you'll lose the water). Don't let the water flow push you in. If these are lava source blocks, you'll get obsidian. Mine it with a diamond pickaxe (only diamond can mine obsidian) and use it to build a nether portal, Check out Minecraft wiki for more tips, and good luck when it comes to battling the Ender Dragon!

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I would say water, put it near the lava and let it flow, then pick it back up and repeat, if you want to mine out All of the obsidian, that will take a while, but you basically have to do the same thing over and over, make sure not to fall into the lava not already cooled into obsidian below the first layer

P.S. @Green Ninja KZX, i have mined a piece of obsidian with a cobble pick before, granted it took about 2 minutes and i didn't get the piece, it is possible to "mine" obsidian with anything, grated you have enough time