Short answer:
The prognosis for feline leprosy is good, but the treatment takes a long time. The sooner any existing granulomas are surgically removed, the better the prognosis.
Long answer:
There is little known about feline leprosy because it's a relatively rare condition and it's very hard to grow the involved pathogens in a laboratory setting. If you wanted to have a stable supply of affected cats to do research on, you'd have to infect them yourself - a practice that was done 100 years ago but that is very restricted by ethical boards nowadays. Add to that the fact that there are established treatments and you simply won't get funding for new studies.
I found this case study Feline leprosy: two different clinical syndromes that only managed to study 13 infected cats in 22 years. Unfortunately, the clinical course was more aggressive in the younger cats and the granuloma and lesions had a tendency to reoccur and spread a few weeks after surgery.
The article Mycobacterium lepraemurium (2012) by the Veterinary Clinics of North America: Exotic Animal Practice sums up that young cats are most commonly infected with Mycobacterium lepraemurium.
M. lepraemurium infections are characterized by rapidly progressive, locally spreading, nonpainful, raised, fleshy, tumor-like cutaneous and subcutaneous nodules. Lesions range from a few millimeters to 4 cm in diameter, with larger lesions usually ulcerated. Lesions can occur anywhere on the body but usually begin as a single nodule or a group of nodules on the head or limbs. Widespread cutaneous involvement tends to occur within 2 months, and regional lymphadenomegaly may be present. Despite the rapid development of generalized skin lesions, dissemination to internal organs does not occur.
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Treatment and Prognosis
1. Complete surgical excision is the treatment of choice for M. lepraemurium infection. Surgery may spread the infection along tissue planes.
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4. The prognosis is best if lesions can be completely excised. Feline leprosy is not considered contagious to other animals or to humans.
The common treatment of feline leprosy is to surgically remove the granuloma in addition to an antibiotic treatment (usually with at least 2 antibiotics) over a course of 2 - 3 months. As with any antibiotics, you must not stop the treatment prematurely, even if the symptoms are already gone. One source (International Cat Care) claims that:
Surgical removal of small nodules may be helpful, but is often not curative, so even if nodules are removed, a minimum of two months follow-up antibacterial therapy is usually recommended.
Such a long-term treatment with several antibiotics can have side-effects like loss of appetite and diarrhea. You can buy feline probiotics to counter the effects of the antibiotics. Please read Do cats benefit from human probiotics? to see why you shouldn't give human probiotics to cats.