Oh! The things I learned when researching this after spotting it in May Street.
The first piped water supply for Belfast originated in a spring just beyond Stranmillis. It was dammed ( as Lester's Dam ) with assistance from the Charitable Society which also contributed financially to the building and upkeep of the aqueduct. By some route I have not yet discovered this ran across to the Dublin Road, down Conduit Street ( so that's the reason for the name ) and thence a small pond at what became the Ormeau Baths. Originally that road was known as Basin Street and wooden pipes led off in various directions towards the recipients.
In 1840 the Belfast Water Commissioners were established and bought-out the dam and infrastructure.
Incidentally, about 20 years later they bought the Richardson & Owden warehouse in Chichester Street to become their headquarters.
However Lester's Dam could not accommodate the growth of Belfast and eventually the Water Works were established in the area between the converging Cliftonville and Cave Hill roads. Artifacts
Even that proved short-lived and money had to be found to commence the Mourne Scheme in 1897, which would take another six decades to complete...