Hi, Jan,
Happy New Year ! - but sadly there is an error, somewhere.
There are several Martins in LPS records, but no Martin (at all) born in 1833, leaving in 1879 or dying in 1893.
The nearest (chronologically) are the following two (which are so similar that they also suggest an error, somewhere):-
Martin, T (i) Born 1825, licensed 1842, retired 1880, died 1882
Martin, T (ii) Born 1825, licensed 1844, retired 1880. died 1882
But there is no record of a Joseph Martin or a J Martin whose dates fit anywhere near those which you mention.
There are, however, the following other names:-
G Martin
JAE Martin
JR Martin
James Martin (x2)
John Martin (x2)
but all are of substantially different dates.
Hope this might help. Do you have a date for which your Joseph Martin might have been issued with a licence? Or any other information as to his career? It is possible (just) that he might be missing from the LPS records.
Best,
BY