A pauper's grave, or common ground, means that it was a plot owned by the parochial board or nowadays, the local authority, which was used to bury people who died in poverty. The grave is filled-up with (usually) unrelated people and when full, a new grave is opened. Dressed ground would have been a term used for private lairs.
The fact that you have proof that your great-grandmother is in a lair owned by, presumably, a family member rules it out of being a pauper's grave.
