I had wondered the same thing but never looked into it until recently. yes, pets and livestock can and do get lymes.
"2.15 Can pets get Lyme disease?
The Lyme Disease Foundation states that pets can get Lyme disease, and the
illness can affect individual pets quite differently. Some animals may
display few or no symptoms; others may develop fever, loss of appetite,
painful joints, lethargy, and vomiting. If left untreated, the spirochete
may damage the eyes, heart, kidneys, and nervous system. Lyme disease has
been diagnosed in dogs, cats, horses,
goats, and cattle. Other species may
also be at risk. For more information, contact the Lyme Disease Foundation
(LDF) and request their free brochure titled, "Lyme Disease & Pets." Lyme
Disease Foundation, One Financial Plaza, Hartford, CT 06103, or 24-hour
Hotline: 1-800-886-LYME (5963), or E-mail:
Lymefnd@aol.com"