There was a wartime Act of 1914, that required foreign nationals to register with the police, then a 1919 Act which extended the purpose. If Dora, with or without his parents, arrived in Dundee sometime after his birth (ie rather than having been born anywhere in Britain), as part of the large influx of Italian immigrants to Scotland in the late 1800s and early 1900s, It may be worthwhile asking via:
https://www.dundeecity.gov.uk/service-area/corporate-services/democratic-and-legal-services/archivesif it is possible to have a search done of the following record set, which they apparently hold:
Dundee City Police registers of aliens, 1917-1949 (class TRC)
Also, this map may be helpful in narrowing down potential regions in Italy:
https://maps.nls.uk/projects/italians/And of course, if the lady your friend is helping was willing, a DNA test may open up even more avenues of research, especially if it highlighted that she did indeed have Italian ancestry.