The Assembly Mall mentioned in the Limerick song was demolished in 1820/20. It was rebuilt as Charlotte's Quay in the 1820s. This suggests thee Limerick song is pre 1820 and much older than the Liverpool song.

The other locations mentioned in the Limerick song still survive.

Limerick Strand is now Clancy's Strand renamed after the Mayor of Limerick George Clancy murdered by british auxilaries during the war of independence.
Gabbets Grove is now known as The Grove and is situated in the Corbally suburb of Limerick.
Thomondgate is an area of Limerick directly opposite Limerick Castle.