Some Liver Spots do go away some overtime but really the liver spots only fade some and do not really ever go away fully.
Once you get liver spots it can be hard to get them to to go away at least fully but you can do some things to help them look like they disappeared.
You can help get rid of the liver spots by applying prescription bleaching creams (hydroquinone) alone or with retinoids (tretinoin) and a mild steroid might gradually fade the spots over several months.
Some other things that help with Liver Spots are chemical peels, laser treatment, Dermabrasion and Freezing of the liver spots at a doctor.
Lemon Juice is a good home remedy for treating and getting rid of Liver Spots at home since Lemon Juice is a natural bleaching agent that pretty effectively fades liver and age spots.
You will have to apply the lemon juice daily at least a few times per day and it can take a month or even 6 months to make the liver spots disappear fully or at least partially.