It is relatively easy to treat localized calcium buildup with a biopsy or minor surgery. However, diffuse mineralization has no known cure. Treatments tend to focus on management of a primary condition or on easing any respiratory distress.
Surgery
If there are localized calcium nodules in the lungs, it is possible to remove them in a minor surgery, provided they are only in one or two locations. This is not a viable option for diffuse mineralization. Surgery may be worthwhile from a cost and invasiveness standpoint if it is able to be done in a few hours of outpatient surgery. However, the more complicated the surgery, the higher the risk and the cost.
Cancer Treatments
Metastatic lung cancer or other cancers can have calcium mineralization in the lungs as a secondary symptom. If the cancer is treated, it may cause a reversal of the mineralization, or at least it will stop additional calcium deposits.
If your cat has an adrenal tumor causing high levels of cortisol, then removing the adrenals may solve the issue, and can often be much easier to solve than metastatic cancer.
Antifungals
Fungal infections may cause calcium buildups in the lungs of cats as well as the other organs and soft tissues. Though they can be time-consuming and difficult to treat, there are antifungal medications that are not overly expensive and which only require you to give your cat oral medication one to three times daily.
Corticosteroids
Calcium buildup is often linked to autoimmune diseases, and it can be lessened by regular doses of corticosteroids. The duration of time and dose of steroids will depend on the severity of the case and the advice of your vet.
Respiratory Aid
In some cases, the buildup may be considered untreatable. If this is the case, the vet may offer some form of medication to either ease pain or aid breathing. The goal, in this case, will simply be to make your cat as comfortable as possible.