From the CD of Bristol Apprentice records published by the Bristol FHS. It doesn't give much more detail. The full entry is:
APP FORENAME, APP SURNAME, FATHER FORENAME, FATHER TRADE, FATHER ABODE, DATE, MASTER FORENAME, MASTER SURNAME, MASTER TRADE, WIFE FORENAME
JOSEPH WILLIAM, JAMES, JOSEPH, CONFECTIONER, BRISTOL, 08-MAY-1837,THOMAS, LUCAS,CONFECTIONER, JEMIMA
There's also this one, which may be a cousin
EDWARD VAUGHAN, JAMES, EDWARD VAUGHAN, CONFECTIONER, BRISTOL, 29-DEC-1835, THOMAS, LUCAS, CONFECTIONER, JEMIMA
More important is this one, which I missed before:
JOSEPH, JAMES, JOSEPH, POTTER, BRISTOL, 07-APR-1812, SAMUEL, LUCAS, CONFECTIONER, ELIZABETH
In 1820 Joseph James, confectioner, became a Burgess of Bristol, having been apprentice to Samuel Lucas.
There were three Joseph James apprenticed in the 1770s, who could possibly be your Joseph's father, but none of them were training to be potters.
Samuel Lucas appears to have been the father of Thomas Lucas. So Joseph certainly started working for the Lucas family, but he could have worked for himself later, or moved to a different firm such as Fry's.
Have you seen the book of Joseph's poetry? It may have some details of his life.
David
PS. I've found a copy of the book now
https://play.google.com/books/reader?id=NrgsAAAAYAAJ&hl=en&pg=GBS.PP10Unfortunately it seems to be missing part of the preface, but what's there shows that in 1841 he was out of employment and contemplating moving to London. The 1851 census shows he stayed in Bristol and was then a foreman at a confectioners, but no indication of which confectioner.