In the year 1377, David Botiller, one of the citizens of Limerick, complained to the lord justice against the provosts and bailiffs of Galway and Athenry, stating, that notwithstanding, amongst other charter liberties granted to that city, it was particularly provided that the citizens and their successors should, for ever, be free of all customs for their goods and merchandizes in any place either in England or Ireland, where they should bring them for sale; yet those magistrates, from time to time, exacted divers heavy customs from him and his merchants, who frequently came with goods and merchandize for sale to the said towns. They were commanded by letters of the lord justice, dated at Tristledermot, 18th May, 1377, to desist, under heavy penalties, from making those exactions for the future; and thus was thrown open to the inhabitants of Limerick a freedom of trade in the port of Galway, which those of the latter were not entitled to in that city. (Hardiman)
A few years later (1377) a Limerick citizen successfully took the authorities of both Galway and Atherny to court over levying murage on him when he was exempt (Hardiman 59). (Thomas)
The action was not specifically about murage. I don't known of a charter that specifically exempted Limerick from murage. Thomas seems to have gone a bit far in her reading of Hardiman here.