The lava moves to where it cools.
Aidan,
By then there's absolutely no biological hazard left ! Some "scientist" will probably say there will be but I'm certain it will be a billionth less polluting than not being burned & mixed with molten rock ! With some luck it might even end up as "rare Earth".

Aidan,
At least you didn't write Larva as one of Qld Ed. teachers corrected it to in a drawing of an indigenous 9 year old girl in a community when she wrote Lava !

individual,
What do you base that assumption on? Are you forgetting the waste would float in the lava?

As for "rare earth", that's not what it means. Rare earths are specific elements: scandium, yttrium, lanthanum and all the lanthanides.

waste would float in the lava..
Rare earths are specific elements
Aidan,
Are you sure or are just not in favour of trying to solve the medical waste problem.
Are you sure they won't be in a Million years ?
It doesn't matter if it takes longer than your patience as long as it reduces the waste !

Aidan,
I have never seen lava nor even a volcano, I've only ever seen that on TV. What can be deduced from such footage is that anything in the way of a lava flow isn't there anymore afterwards. What'd be the reason to think that medical waste would remain even after days of tumbling around molten, burning & glowing hot rock ?

By the time the lava cools the waste will be turned to minute particles of ash and set in rock, any germs etc., will have long gone.