The major cause of death from cancer is metastasis. In the lung, metastases can form in the lymphatic vessels or the lung parenchyma. The presence of cancer metastases in the lung lymphatics indicates poor outcome and rapid disease progression in patients. This is recapitulated in a mouse model, where breast cancer metastases in the pulmonary lymphatics grow larger than metastases in the lung parenchyma, without vascularization. To explain rapid growth of metastases in the lymphatics in the absence of angiogenesis, we have developed a 3D mathematical model of intralymphatic tumor growth. This is a deterministic continuum model based on partial 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 oxygen levels to remain relatively high throughout the tumor. The greater diffusion coefficient of oxygen in lymph further improves oxygenation of intralymphatic metastases which rarely become hypoxic. Improved tumor oxygenation leads to decreased tumor cell death and a rapid increase of metastatic burden in the lymphatics. Importantly, our model further predicts that the kinetics of growth of intralymphatic metastases are exponential. This contrasts the established view that all tumors follow Gompertzian growth kinetics, i.e., that tumor growth rate decreases as tumor size increases and that angiogenesis is required for progressive growth. These findings explain rapid growth of metastases in the absence of angiogenesis and indicate that the lymphatic niche is a favorable environment for metastatic growth. Our predictions also suggest that therapeutics targeting intralymphatic tumors should be optimized to the specific tumor microenvironment.