There is no evidence that I have come across (to date) to suggest that the Limerick Clothing Factory supplied Irish Volunteer uniforms, however it is possible that they may have done so. But, there is documentary evidence that the Limerick Clothing Factory in 1922 was the supplier that won the £40.000 contract to supply military uniforms to the newly formed Irish National Army.
There is a good deal of information on the Limerick Clothing Factory on the internet. Check out this article for example: https://www.limerickcity.ie/media/clothing
The button on sale here is most likely a button that was worn on the tunic of an enlisted man in the Irish National Army circa 1922. Therefore, this particular button is probably the very first official pattern Irish Free State Army (National Army) button based on the fact that the Limerick Clothing Factory was awarded the contract in 1922 by the newly formed Irish (Dáil Éireann) Government.
This brass other ranks button is 25mms in diameter, broad harp with eight strings. The retailers name on the reverse is “THE LIMERICK CLOTHING FACTORY LMtd”
Interestingly, these Limerick buttons are about 1mm smaller (in diameter) than the John Ireland and Todd Burns types described above.