You just said the basset hound cannot get off of the antibiotics so are you wanting to replace them or add an herbal supplement?
I go through this a lot with my friend who doesn't believe in medicines as we know it and uses herbs for everything. She never even was vaccinated for school and had to sign a waver about it or they would not let her attend. She is an herbalist and brings me over a number of things every time I am sick or not to try. I've seen her sick to death and no matter what, she will not even take an aspirin. Instead she will make herself up a homemade remedy.
So in the first place you have to decide if you want to go from a prescribed medication from a licensed vet to using an herbal supplement. Weigh your risks.
Keeping an open mind about medication VS herbal supplements, my son had to be on medication all his life and we had issues of side effects so at one point we went the herbal route for about two months. We had an expert in the field guide us to what he thought was the perfect combination of stuff plus we changed his diet too to a lot of natural stuff. Didn't help at all and we went back on medication again until we found another herbalist that suggested another combination of things for us. I won't tell you the end result so you can make a decision on your own but I will say that lyme disease in humans is a very scary thing and it will depend on what risks you want to take.
Now just to throw you off even more, on a very positive note, I am what you would call a nervous wreck. I suffer from post traumatic stress disorder after the death of my son. I threw away my tons of antidepressant drugs years ago and I totally drink herbal tea when I have a meltdown and need to calm down.
Best wishes and good luck.