Is it true that breast lump or tumor have been in your breast for a year or two and a mammogram can see them?

Yes, even longer. Yes, actually breast cancer begins as a single cell and probably requires 10 years of growth to become approximately 1 cm in size. This is when it will first be revealed during an exam by the doctor. While a mammogram may pick it up slightly sooner it is certainly the fact that the mass has been there for many years prior to its discovery with mammographic imaging.
Yes, cancers begin at the cellular level and may take several years before they get large enough to be visualized on a mammogram.
Yes. Some breast tumors, even cancers, are slowly growing and may have formed a year or even two before it became large enough to bee seen. It may be easier to understand this by knowing that a tumor the size of a small pea already has over a billion cells it.
Yes. A breast lump can be seen as small as 3 or 4 mm in a fatty breast , but may be larger before it is discovered in a dense breast, as most breast lumps of concern are of similar density to glandular tissue. The benefit of a mammogram is to find a cancer prior to it becoming palpable to you or your doctor.