Radiotherapy uses X-rays for treatment. You must have had a chest X-ray taken one or more times. The X-rays used in radiotherapy are just the same, except that they are of much higher energy.
X-rays kill tumor cells by causing damage to their DNA. DNA is the most important part of the cell, because the entire code that makes the cell function and multiply comes from it. X-rays can cause breaks in the DNA and makes it impossible for the cell to multiply. Unless tumor cells multiply, the tumor cannot grow. Some lymphoma cells kill themselves when their DNA is too badly damaged. This is called 'apoptosis'.
The normal cells of the body are mostly protected from DNA damage by X-rays. This is because X-rays mainly cause damage to cells that multiply very quickly. Most of the normal cells in the body dont multiply fast. But tumor cells do. That is why they are more sensitive to damage by X-rays.