There is evidence of "Post-Treatment Lyme Disease Syndrome" [1].
> Several recent studies suggest that B. burgdorferi may persist in animals after antibiotic therapy.
There's also evidence that the standard Lyme treatment increases the "round bodies" form of the bacteria [2].
That being said, there's still a lot of shysters who, as you say, push long-term antibiotics or diagnose patients with "Lyme disease," despite not having evidence.
The CDC recognizes the existence of "Post-Treatment Lyme Disease Syndrome," but highlights that long-term antibiotics aren't a good solution [3].