The lymphatic system is well recognized as an important pathway for cancer dissemination; moreover, many types of cancer can form large lesions in tumor-draining lymphatics and in the lymphatic vessels in distant organs to which they have spread. Involvement of lymphatic vessels with cancer is one of the most important negative prognostic indicators. It is not understood what impact the lymphatic microenvironment has on the growth of metastases. To explain rapid growth of metastases in the lymphatics in the absence of angiogenesis observed in mice and in humans, we have developed a 3D mathematical model of intralymphatic tumor growth. This model is based on deterministic differential equations used to describe avascular tumor growth, adapted to reflect the unique architecture of the lymphatic vasculature. Our model predicts that the cylindrical shape of the lymphatic vessel, which constrains growth of the tumor in two dimensions but allows indefinite growth along the vessel, enables higher oxygen levels throughout the tumor. The greater diffusion coefficient of oxygen in lymph further improves oxygenation of intralymphatic metastases. Improved tumor oxygenation leads to decreased tumor cell death and a rapid increase of metastatic burden in the lymphatics. Importantly, our model predicts that growth of intralymphatic metastases is exponential. This contrasts the established view that all tumors follow Gompertzian growth kinetics. These data explain rapid growth of metastases in the absence of angiogenesis and indicate that the lymphatic niche is a favorable environment for metastatic growth.