Just some thoughts (and I realise you may have already pursued these):
For the Norway link, have you considered having a look in the area of Norway mentioned on the IGI record of a Lorents Andreas Eid b 1815 at Ytteroy, Nord Trondelag, Norway? I know it is not your Lorenzo, but looking sideways, it is in right timescale (ie with your Lorenzo born c1802) to be a cousin having been given the same 'family' name of perhaps a grandfather.
Also, as Sarah Lynch's parents are buried in the grave with her and Lorenzo, have you managed to track down anything on them that may give a clue to where they lived and/or worshipped (in the hope of eventually finding Lorenzo and Sarah's marriage details in some old church records at PRONI which may give you more info on Lorenzo).