The forum's more experienced members will undoubtedly be along shortly to share their experience.
In the meantime, don't delay in booking a hotel - the entire plane-load full of passengers will also be looking for overnight accommodation. BA will certainly reimburse up to the amounts stated in the email you received, and even more if you can show that you necessarily had to spend more than that.
The fact that BA specifically mentioned "lightning strike" suggests that they will contest compensation claims, but deal with that later.