So I've just trimmed back my lavender bush and realised that underneath the healthy green leaves its almost entirely black and crispy. Nothing has changed with the routine - its been trimmed regularly and is in a dry sunny spot and otherwise has been growing fine. The branches near the top are bendy and healthy looking and have a green inside when broken, but the ones nearer the bottom are dry and brittle. Is the bush completely dead at this point or can it be recovered?

It looks pretty bad! I also looks rather old. But you can't always tell. If there is green anywhere, it just might come back.
I'll just go check my very old lavender for comparison. Be right back. Nope. Brown and brittle underneath, but no burned-looking leaves, and the tops all have flower-spikes.
Your lavender may, indeed, be dead. But I would still try one more thing:
Wait a week to see if there is new growth and cut away the parts that don't show any. If there are none, cut it down to the ground. It might grow back from the roots. (long shot)

Afterthoughts. It looks as if there might be some green shoots at the bottom. You can cutting them and propagating new plants https://www.gardeningknowhow.c...
And remember, in future, not to prune too far back: leave some green at the ends of the branches when you cut them back.