Tumors are unfortunately very common in rats, especially when they start to reach old age (1.5-2 years). They, along with many other rodents, are especially suceptible to mammary tumors in females (males are as a whole less prone to tumors).
These tumors will usually present as a small lump or hard spot on the flanks or belly of the rat that can grow surprisingly large over time. These tumors are typically benign and only pose a threat once they become large enough to impede the animals movement or breathing.
Treatment for these types of tumors is typically palliative in nature; it is nearly impossible to remove a tumor once it begins to grow, and a rats fragile body precludes it from being a candidate for more aggressive forms of treatment that may work on a human (radiation). The best thing to do is to keep them happy and comfortable. Most rats can live on with very few, if any at all, limitations or pains for quite a while after a tumor becomes apparent. Once the tumors becomes large enough to cause discomfort for the animal, the best route is typically to consider euthanasia.
As along time keeper of rats, I know how hard it is to let one go. They pack a lot of personality into just a couple short years. I've lost too many to mammary tumors, it's unfortunate that they are so prevalent.