The problem with antibiotics at least in some countries is that official guidelines take the position that chronic Lyme does not exist, and thus doctors are forbidden to write long-term prescription to antibiotics for Lyme. Short-term may not work, as research suggests that antibiotics works only on some phases of the life-cycle of borreliosis and only for some co-infections.
Chronic Lyme where the bacteria persists does not exist. There is no evidence the primary bacterial infection persists as far as I have been able to discover. So, that is a faulty starting point in terms of your framing. Now, what is chronic lyme, does the bacteria injure the nervous system, does it leave "debris" behind that maybe antibiotics somehow help the immune system attack and clear? That is way less clear and not validated medical science.