The research I did at the time this happened seemed to indicate that children under six months of age may not make enough stomach acid to kill the spirochete, but around six months of age the stomach acid ramps up, and transmission does not occur after that time. This conclusion was based on studies they did in mice.
I also ended up remembering that hunters have eaten rare deer meat without getting lyme, which supports the theory that stomach acid destroys it. For us, the lyme was coming from the blood of our dog, which my baby had swallowed, so eating rare deer meat was an apt comparison, and made me feel better. FWIW.
He hasn't had anything that seemed like lyme symptoms since then, although I did treat him for intestinal parasites (because I had parasites, and because I remembered that he could get intestinal parasites from a dog's blood). When I treated him for intestinal parasites, some rashes he had cleared up, he gained some weight, and the circles under his eyes disappeared. I don't know whether he got the parasites from me in utero or from swallowing the dog's blood, but it seemed he had them. Hope this helps!