I can understand your confusion because lithium is normally used in treating biplor depressed patients. However it has a major impact on the body's handling of electrolytes and salt. As I understand it your son has a problem with salt imbalance.
So I think that your doctor is trying to alter his salt metabolism with the lithium. This may be the only option he has left because it is not a common use of lithium.
However I do think that the doctor could have explained this better to avoid this worry. As lithium is a drug which needs very careful handling then I think you need to sit down with the doctor and talk about exactly what he is trying to achieve and what you should now do about his salt intake and fluid balance. These need to be tightly controlled. Also some drugs like ibuprofen are not really recommend when taking lithium so you need to know what else to avoid.
I would continue with the antibiotics as secondary infection is always a risk in patients like your son. You need to finish the course to avoid problems with resistance.
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