A requirement of the 1881 graveyards act was that a Sexton be employed - prior to this the family had been responsible for digging the grave in many yards. Such graves were usually within a family (or Quarterland) plot.
Thus if after 1881 there is probably a sexton's book - I have seen one (I think for Braddan New) in Manx Museum - there may be others there or more likley with the current sexton for the yard.
Prior to this date I suspect you may be unlucky - there are very few extant markers left at Lonan Old yard; Lonan New just above Laxey is well organised but some markers must have been brought here from the old church as I have photos of some that bear dates prior to 1834 date of erection of church. The older markers appear to be in rough date order and concentrated around the entrance path to the church but obviously families would obtain larger plots for subsequent use and Laxey had in the late 19th century a high population.