I can see a transcription of a baptism at St. Mary's Belfast on 20 May 1883 for a Mary Jane "Marran" for parents Robert "Marran" and Mary "Monaghan" of 5 Chapel Lane (there's that address again), the sponsor was Mary McCormick, I wonder if this is a mistranscription of Robert Morrow and Mary Malaghan? Unfortunately, not available to view on the NLI RC parish records website. Can't see a civil registration either. I was hoping to track Robert and Mary forward, for example, to see them in the 1901 Ireland Census (Mary's birth place would be nice to see).
Anyhow, here are some listings for Chapel Lane in the Belfast Street Directory:
1880: 5 Malaghan, Mrs., green grocer
1884: 5 Monaghan, Susan