I believe this to be John & Elizabeth's son William. His children's names, make the 1785 marriage of his possible grandfather look more likely. Maybe some of the records for Williams siblings are missing?
1851 Orton, Cumberland, all born Carlisle. No Marriage?
William Mckenzie 27 (1824) Pot Dealer
Jemima wife 22, John son age 3
1871
https://www.familysearch.org/ark:/61903/1:1:V51K-XXB?lang=enGRO registrations, mother MCKENZIE/MCKINZIE/MCKINZEY
MCKINZIE, JOHN
GRO Reference: 1848 M Quarter in CARLISLE Volume 25 Page 72
MCKENZIE, EDWARD
GRO Reference: 1851 D Quarter in CARLISLE Volume 25 Page 68
MCKINZIE, WILLIAM
GRO Reference: 1854 S Quarter in COCKERMOUTH Volume 10B Page 438
MCKINZIE, JAMES
GRO Reference: 1857 S Quarter in COCKERMOUTH Volume 10B Page 435
MCKINZEY, ELIZABETH ANN
GRO Reference: 1862 S Quarter in COCKERMOUTH Volume 10B Page 495
MCKENZIE, ANNIE ELLEN
GRO Reference: 1872 J Quarter in WIGTON Volume 10B Page 498
By 1881 William senior is a widower. Daughter Ann on census
MCKINZIE, JEMIMA died age 49
GRO Reference: 1877 S Quarter in COCKERMOUTH Volume 10B Page 313
Colin