1894 Thom's Directory of Dublin lists two W. Lemons, but neither in the business type you mentioned :
William Lemon esq., 31 Grosnover Rd, Rathmines
Mr. W.R. Lemon, 5 Seville place
there's also
Maxwell Lemon, confectioner, 14 Nassau Street
Lemon & Co., wholesale confectioners, 30 Bachelors Walk
In the 1904 edition the Bachelors Walk business is not listed, and the entry at Nassau St the business owner is shown as
Mrs Maxwell Lemon. The trades index shows this same address as Miss Lemon with a residence at Castle Ave, Clontarf
I dont see a listing for a death of a William Lemon in Dublin around the right time.
Is this the same Lemon family as mentioned in your other post on the Cork board ? (see :
Dora Lemon )
Shane