It says on the Articled Clerkship document that John's father was Thomas Richardson of White House, Morland.
It's probable that he would serve under Thomas Briggs at Appleby, one of my relatives served under an Attorney at Penrith and served his apprenticeship there and married there.
It might be worth looking on the Trade Directories around the late 1820s/early 30s to see if there is a John Richardson listed as an Attorney at Appleby.
The best way forward would be to view the original parish registers, for the marriage that you saw at Appleby and also the baptism of John to see if his father's residence is mentioned - ie White House. As his father was a 'Gentleman', could he also have been an Attorney? Also worth looking at the Parish Register for daughter Mary Ann, as it may mention father's occupation.
Is there a Will for John at all around the 1830s at Appleby? It may be worth looking on CASCAT.
If you are unable to view the original parish registers of Morland and Appleby you have an option of visiting your nearest Latter Day Saints Library, ordering the relevant parish register films, and I think you have about 3 months to view them, for a small fee. Wherever you are in the world, there is usually an LDS Library nearby.