Lynch is an Irish surname and, as far as I know, only individual people have coats-of-arms, changing with each generation. Families have crests and badges. Someone may know much more. The quote below is from Wikipedia.
Lodger.
"In the heraldic traditions of England and Scotland an individual, rather than a family, had a coat of arms. In those traditions coats of arms are legal property transmitted from father to son; wives and daughters could also bear arms modified to indicate their relation to the current holder of the arms. Undifferenced arms are used only by one person at any given time. Other descendants of the original bearer could bear the ancestral arms only with some difference: usually a color change or the addition of a distinguishing charge. One such charge is the label, which in British usage (outside the Royal Family) is now always the mark of an heir apparent or (in Scotland) an heir presumptive.
Because of their importance in identification, particularly in seals on legal documents, the use of arms was strictly regulated; few countries continue in this today. This has been carried out by heralds and the study of coats of arms is therefore called "heraldry". Some other traditions (e.g., Polish heraldry) are less restrictive — allowing, for example, all members of a dynastic house or family to use the same arms, although one or more elements may be reserved to the head of the house".