Almost all of the several hundred Ulster newspaper references I can see to Lower Grosvenor Street are to the street at the SE corner of Grosvenor Square in London and these peter out after the 1860s (presumably when the London street became just Grosvenor Street).
There are literally only a handful of newspaper references to Lower Grosvenor Street relating to Belfast, probing a couple of these further, I discovered that one wasn't so much stating a Belfast street name as it was indicating an area at one end of Grosvenor Street, ie. the Lower Grosvenor Street area of Belfast and the second was a mistake, namely someone with the distinctive name of Robert Conroy of 28 Lower Grosvenor Street in an 1897 newspaper item, whom I was able to readily find at 28 Little Grosvenor Street in a contemporary street directory.