I would be worried the heat would melt the drone even if nothing hit it.

It survived, per a UK news interview with the pilot: https://youtu.be/dFUa8yAnD6s?t=77

I'm no expert but I don't know if you could recover the HD version of the footage without the drone coming home, perhaps only the FPV version. Happy to be corrected though.

With DJI FPV, you can get a recording of the HD signal in the goggles. It's not as good as a GoPro/action cam footage recorded on board, but infinitely better than what ground-recorded analog FPV footage looks like.

Also possible for the drone to fall into lava and still transmit for a few seconds, maybe enough to get the higher-quality buffer?

Highly unlikely you'd have time to transmit footage. Various chips in the drone would go into thermal shut down at 90 C ish. The lithium battery would probably explode shortly after.

The scene from Terminator II came into my mind!

the appropriate time scale would more likely be milliseconds