This is what I could glean with a quick look through the online newspapers that I could find. His death appears, as well as the death of his son, John. However, his marriage did not appear in the search results for 1828-1830. I just included any mentions of a Dodgson in Casterton. Perhaps you'll find his father (Rowland, maybe)? Hope this helps.
Westmorland Gazette, Saturday, 24 Jul 1830
MARRIAGES
On Saturday last, at Sedbergh, Mr. John Dodgson to Miss Betty Taylor.
Kendal Mercury, Saturday, 01 Jun 1839, page 3
At Casterton, on Wednesday week, very suddenly, Mr. John Dodgson, in the prime of life.
Kendal Mercury, Saturday, 16 Nov 1839, page 3
On Wednesday last, in Highgate, Elizabeth, second daughter of the late John Ddogson, Esq., aged 7 years.
Carlisle Journal, Saturday, 13 Jul 1844
At Kendal, on Friday last, aged 21 years, Roger, son of Mr. Dodgson, of Casterton.
Westmorland Gazette, Saturday, 06 Jul 1844
Yesterday, in Finkle-street, aged 21 years, Roger, son of Mr. Dodgson, of Casterton. Deceased died from the bursting of a blood-vessel in his head.
Westmorland Gazette, Saturday, 09 Mar 1833
At Casterton Fell Gate, Thursday se'nnight, Mr. James Dodgson, aged 24.
Kendal Mercury, 26 Jul 1845
DIED
At Casterton, near Lonsdale, Saturday night last, Mr. Rowland Dodgson, aged 66.
Westmorland Gazette, Saturday, 19 Nov 1853
DIED
On Friday last, at Fell Yeat, near Casterton, John, son of Mr. William Dodgson, aged 38 years.