A boat with the "Invulnerable" NBT tag does not get destroyed in lava, but it doesn't float like one would expect.
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So, when you push boats onto lava on a diagonal, the boat floats in lava. When you decide to get in it, it floats to the bottom and doesn't break. It's hitbox is such that you can stand on it and receive damage which is lava damage, but not catch fire. The image with the lapiz blocks show where you cannot place blocks because there is a boat in the way. Kinda funny because boats are 2x2. Also, I was able to get the boat to float in land by sitting in it. It's hitbox is still above the ground. My y-axis was hoveering between 4.3 and 4.5 while standing on the hitbox.
Upon saving , quitting, and reloading the boat was again floating above lava. However, it was being held up by another block.
Lava is not water. Unfortunately, minecraft's simulation of lava is not only inconsistent with reality (like virtually every other video game with lava), but also inconsistent with the consistently inconsistent portrayal of lava in fiction.
You probably shouldn't be able to swim, or even sink, into lava. It's more like sand, except ridiculously hot. It's molten rock.