According to the Lagan Canal Trust,
The Lagan Navigation also forms part of a wider all Ireland waterway network. This network of waterways once traversed through the towns and cities of Ireland delivering goods and produce, helping to shape the economic fortunes of the country.
I would be grateful for information about any goods or produce that were ever carried from the Shannon, or from the Royal or Grand Canals or the River Barrow via the Shannon, through the Junction Canal in the Ballinamore & Ballyconnell Drainage District [later called the Ballinamore & Ballyconnell Canal and later still the Shannon–Erne Waterway] and then the Ulster Canal to Lough Neagh or any of the waterways connected therewith. Or, of course, in the opposite direction.
As far as I can tell, outside the sales blurbs written by engineers seeking employment and waterway owners seeking subsidies, there was never a connected all-Ireland waterways network; nor was there ever any need or demand for such a thing.
Any more than there is now.