Looking at Welshnewspapers online, I can see an Alexander Lawrence, photographic artist, at 80, Queen Street between 1893 and 1895. Alexander died 31st Dec 1894 and his death notice was in the Western Mail, 3 Jan 1895.
J. Lawrence (the name on the photo card) , photographic artist, 80 Queen Street, is mentioned in the Evening Express, 20 August 1895. I cannot find reference to a photographic establishment at that address after this.
There are references to its being a licensed premises/eating house after this date and in the 1901 Census it is described as a restaurant.
I can find Alexander in the '91 Census but puzzled who "J Alexander" might be.