Hi
This is a difficult one.
Lower Agbrigg was formed in the 1939 and it had parts of Wakefield and Dewsbury in it.
The main areas I think were Horbury, Ossett, etc. The registers were then divided and sent to Leeds and Wakefield.
The burial or cremation would depend on were the lived, if you have an address it could point you in the right direction. The obit if there was one would have been posted in the local paper so you really need to know what part of the area they were from and that might involve getting the death certificate from the General Register Office in Southport but I always fell I have been ripped off when I get one from them.
A long shot could be going on the Wakefield website and seeing if you can find them in the on-line burial registers.
Regards
John