Humans are pretty much water. They have a density of 1 ton per m³. Lava on the other hand has a density of more than 3 tons per m³. You'd not sink... you'd stand on the surface of the lava and get turned into burning charcoal from the feet upwards? No, your skin gets vaporized and charred even before you touch the lava... It's an agonizing and horrible death.
Lava Damage in the 5e DMG
Of course, the Dungeon master's guide offers damage on page 249:
10d10 / round wading through a lava stream
18d10 / round Being submerged in lava
With a tiny fix
Which needs some correction and then still can stand: simply replace the wading through with walking over (since you don't even make a depression in the surface), and make the latter being doused with Lava.
Oh, if you get in a lava shower, remember that that stuff is heavy. So it would be fair to add some bludgeoning damage from the impact of the molten rock to the body - which sounds about like a collapsing roof (DMG page 122, example trap) for 4d10 bludgeoning damage atop of the 18d10 heat damage from just having been doused in molten rock.
Oh, and for the record: the very same damage also would apply to molten metals.