Hi
there is a newspaper report in the Carlisle Patriot of 1838, about the removal of a pauper, William Kennedy, which you might find useful.
amongst all the evidence listed a Leonard Kennedy said:
Leonard Kennedy – I am 80 years old and better. Simon Kennedy was my uncle. My father’s Christian name was Tom. I was brought up at the High Moss Thorn, which was kept by old John Kennedy, my grandfather. Simon lived there with his father till he was nearly 20 years old. He married Jenny Forster when he was about 25; and they had in their family a son named John. John had afterwards a family; his son William is the pauper in this case.
Is this your Leonard? Possibly the one buried at Stapleton in 1844 aged 86, of Walton. If so, he confirms his father was Tom Kennedy, grandfather John Kennedy and uncle Simon Kennedy.
Looks as though his baptism might be in Bewcastle in 1759? You'll have to check the parish register to see if there are any other clues to confirm his family
best wishes
robbiesmum