I am sorry I keep labouring this but does this mean that the lady must have appointed the solicitor as executor with the financial implications of that - their fees.
The solicitor most likely suggested himself as executor when he drew up the will, which could have been a few years ago.
Given that we now know the lady was probably living in sheltered accommodation ( if the address was known by any family member it should be possible to find out what type of accommodation it was)
then it seems possible that the funeral arrangements were made and possibly paid for, by the local authority.
My understanding is that you own the memorial in a churchyard, but never the plot, unlike a cemetery
The church has a lot of rules since 2007 regarding memorial stones, additions can only be made by applying for a faculty, at a cost, replacement must be in line with health and safety, and more, all at a cost, and there may not be funds available.
Hard though it is for the bereaved the problem is that everybody involved, social services, the funeral director, the solicitor and the vicar are just doing their job and have no personal knowledge of the lady and have no reason to hunt through old records, and may be governed by rules of client confidentiality
Mike