My mother has liver spots. Should I be worried for what this means?

Lentigos or seb k's. There are two common skin spots that are often called liver spots, although neither is related to liver disease. The lentigo is like a dark freckle and can vary a lot in size and shape. They can respond to cryotherapy or bleaching. Seborrheic keratoses can look similar but are more varied in color and are usually raised. They often look warty. Cryotherapy may clear these, bleaching doesn't help.
No. Liver spots (lentigines) are a localized darkening of the skin in response to sun exposure. They are no problem in and of themselves, and can be treated with liquid nitrogen in a dermatologist's office. But your mother needs to start applying a good sunscreen lotion every day, rain or shine, to avoid getting more of them.