What would cause my dog to become lethargic and have loss of appetite and balance?

Anything from poisoning, to organ damage, to a bug, to a foreign body.

Please take your dog to the vet.

Start even simpler, Sariss. Dehydration from an upest tummy or overheating can cause those. Even if it's that simple, it's progressed far enough (with the loss of balance) to merit an IMMEDIATE trip to the vet. Now.