Hi Bruce, according to the Monumental Inscriptions for Hamilton churchyard there is only one stone with the name Hamilton and Bell together. It reads -
This is the burying place of James Hamilton and Jean Bell and their children 4th January 1818.
This is more than likely a "marker stone" to safeguard their plot being used by someone else, (there was a lot of it about!) it also may have been when a child was interred, but it most probably is not a date of death for either adult. The next stone to this one simply reads - "The intended burying place of James Hamilton". This would probably be his too, or perhaps his father's. No Lillies or Lillys in the MIs, sorry.
Hamilton had quite a few Scessionist churches (breakaways from the established presbyterian church)and the records, as far as I know, are all at the National Archives of Scotland in Edinburgh. There are huge gaps everywhere and many records haven't survived. There is a baptism book for the First Relief Congregation Church of Hamilton, baptisms from 1776 - 1800, it is at Hamilton Central Library. I have the transcript of it but no Lillies there either. Too many Hamiltons to mention, but none married to Bell appear in it.

Kind regards,
Grangeburn.