No, because that's not an infectious disease like a virus or bacteria. It's an allergy your body develops to a specific carbohydrate (alpha gal) found in pretty much all mamallian meat except apes/humans. A specific chemical in the lone star tick saliva triggers it, so you just need to get bit. There's no virus or bacteria to vaccinate against.

https://en.m.wikipedia.org/wiki/Alpha-gal_syndrome

There is a canine vaccine for lyme disease (different tick species). Human vaccine used to exist but was pulled from market, might be a new one soon though. There are unfortunately other diseases besides lyme disease though that ticks can carry, including rocket mountain spotted fever and anaplasmosis. And while lone star ticks (the meat allergy ones), don't tend to transmit lyme disease, they can transmit other diseases, unrelated to the meat allergy issues.