Hi Karen 
DEATHS -  James HENDERSON  There were 23 "hits" for deaths for persons named James HENDERSON (or James + second christian name) - between 1903 and 25 May 1916 (when Lilly Jane remarried).
After some "fluffin' around"  

 , I've been able to eliminate a good many - but this was based on the supposition that your James HENDERSON was born somewhere between 1865 and 1877.
That then leaves  > > 
1916 / 3309 - HENDERSON - James - 50 years (bc 1866)[Death reg'd. in Christchurch - can't find cemetery record].
1916 / 1168 - HENDERSON - James - (about) 39 years (bc 1877)[Buried at Napier - occupation:  joiner]
ALSO  ... this one (but born circa 1863) ??
1912 / 2180 - HENDERSON - James - 49 years [Death reg'd.  at Christchurch]
Could find only two who died in Auckland area (they were too old) ... and there were no deaths in the time frame, registered north of Auckland (e.g. Dargarville  etc. ) : 

But anyway  ... see next post.   

~  Lu