There is at this time no significant convincing evidence of a connection between MMTV and lymphoma - the question many investigators are asking instead is the potential connection between MMTV and breast cancer.
The mouse mammary tumour virus (MMTV) is a what's called a B-type retrovirus (viruses, like HIV, that are characterized by their ability to convert RNA to DNA during replication in the host cell) and is thought to be the most common cause of breast cancer in mice. However, its role in human breast cancer is very controversial. The claim is in part that MMTV may explain the geographical variation in human breast cancer incidence based on the distribution of MMTV in house mice: thus, breast cancer incidence is very low in Asia and Africa, very high in North America and northern Europe with an intermediate incidence belt in southern Europe and Latin America, so the argument would run, for example, that the incidence of human breast cancer is higher in western Europe, inhabited by M. domesticus which harbors MMTV, than in eastern European lands where a different mouse (M. musculus) dominates. This has suggested to some observers that human breast cancer may have a zoonotic connection - meaning, a disease transmittable from animals to humans - and so, with humans acquiring the virus from mice.
But (1) even though many research groups have detected the MMTV-like sequences in human breast cancers using different approaches, several groups have not been able to do so, and (2) demonstrating the presence of MMTV prior to the onset of human breast cancer has not met with significant success, and if MMTV is not present before BC-onset, then this makes the zoonotic claim relatively unpersuasive (and (3) I among others find the geographical arguments uncompelling). So although there certainly are many observations that suggest a strong association between the two (human BC and MMTV), this is insufficient to deduce a claim of causation, which requires lot more robust and direct-linkage evidence. So we can say at best that the claim of a MMTV retrovirus breast-cancer connection is hypothesis-generating, but at present no more.
My perspective? There are undoubtedly likely to be viral components to breast cancer but there will be much more: environmental /dietary / lifestyle, genomic, immune system and many more. From my research, breast cancer is assuredly a complex hydra-headed evil and my sense is that we must be reductive and go "low" beneath all these components and factors to the level of primitive underlying molecular pathways and processes that are common to the pathogenesis of all cancers as well as "cancer-connected" diseases and conditions, including glycemic conditions like diabetes, lipid disorders, immunosuppressive disorders, and degenerative neurocognitive disorders, among others. That is why there is provisional evidence of antitumor benefit from lipid-control drugs like statins and diabetes / glycemic control drugs like metformin (Glucophage), anti-inflammatory agents like NSAIDs, among many others including the very primitive Vitamin D Receptor (VDR) that in part motivates the advocacy of high-dose Vitamin D3. To borrow a phrase from physics, we ultimately need a "unified theory" (although on the journey I don't mind culling the secrets from more localized and narrower-spectrum investigations and theories).
Breast Cancer Watch