We don’t know who the illustrator is. John Lawrence (1753-1839) did not identify all of those who helped to complete his book. The book where this Suffolk cow drawing came from was published in 1842 – it was one of several editions of A practical treatise on breeding, rearing, and fattening all kinds of domestic poultry, pheasants, pigeons, and rabbits : also, the management of swine, milch cows, and bees, with instructions for the private brewery on cider, perry, and British wine making.
Based on the age of this book, I suspect there was at least an original artist, an engraver and a colorist involved in producing this full-color cow drawing. None of those talented folks were identified.
As is often the case, the name which was used to describe this particular breed of cow has been merged and virtually gone from history. I found one historical reference that mentioned the Suffolk Red Polled cow. Another work, from 1872, mentioned that Suffolk cows were small and “in old times” had horns but that the author did not know anyone who had seen a horned Suffolk cow.
The “old Suffolk cow” was valuable for its milk. The “improved Suffolk breed” was red, still relatively small and valued for its milk.
Regardless of the details of the cow species shown, I think this is a lovely vintage drawing of a brown and white cow with a milkmaid. The maid is wearing a straw hat with a red ribbon and a blue dress. The cow is mottled white and brown and has its horns intact.
This image is copyright free and in the public domain anywhere that extends copyrights 70 years after death or at least 120 years after publication when the original illustrator is unknown.