yeppers
Was Henry stoking a fire when the accident took place?
Was the fire caused by a beam of sunlight focusing through the lighthouse lens?
NO to both.
Okay, is this a correct statement? A lighthouse keeper was inside the lighthouse when an accident occurred where the lighthouse’s normal operating fire started a larger fire which destroyed the lighthouse and killed the lighthouse keeper.
There is something about this so unique and bizarre people talk about it to this day.
Was something stored at the lighthouse that was particularly volatile in a fire?
If the accident wasn’t witnessed, would it have been notable?
YES - there is obviously more to it.
That last question there is hard to answer.
After the fire, there presumably would not have been a lighthouse at that spot, until such time (if ever) as a new one was built. Was this lack of a lighthouse during this time significant?
Nope.
In regard to the other person(s) who was (were) there:
Was it just one?
If this person(s) had not been there, would the accident have happened?
Was (were) the other person(s) employed at the lighthouse?
A social visitor?
A business visitor?
A random passerby?
I’ll try to clarify.
If nobody witnessed the fire while it was burning, and someone came the next day and saw the ruins of the lighthouse, and the deceased victim, would they have thought it a notable event or just a run of the mill building fire?
Was the lighthouse itself well known?
yeppers
Did the fire itself directly kill him?
Is it on record that someone else was there, besides the victim and a witness? Or that an animal was there?
Ah I see my first question has been answered: NO
So, is the unique bizarre thing the way the fire was caused or the way that the fire, indirectly, killed him?
The way it, indirectly, killed him. Having said that, I would explore some of the cause of the fire, etc. But he definitely died indirectly and that is really unique.
Was the proximate cause of death:
Blunt force?
Something piercing him?
Being crushed?
Falling?
Something mutilating him?
Did he drown? 
(I accept that there’s some overlap of terms so more than one can be true)
No to all.
suffocation?
burning?
blood loss?
decapitation?
starvation?
poison?
strangulation?
broken neck?
Nope.
disease?
old age?
natural causes?
No, his death was indirectly caused by the fire.
A burning giraffe fell on him.