The contribution of lymphatic capillaries in the fluid and drug transportation throughout vascularised malignant tissue is qualitatively and quantitatively discussed. Our starting point is the derivation of differential equations for coupled fluid and drug transportation across three physical domains present in vascularised tissue: the interstitium, capillary vessels and lymphatic vessels. We begin from mass and momentum balance equations in each physical domain, which are geometrically characterised by the inter-capillary distance (microscale). The Kedem-Katchalsky equations are used to account for blood and drug exchange across the vessel walls. Employing asymptotic homogenisation, we can formulate a multiscale model which allows for macroscale variations of the microstructure, under the regular assumptions such as local periodicity, accounting for spatial heterogeneity of the angiogenic nature of the capillary and lymphatic networks. At the macroscale, the fluid dynamics are governed by a triple coupled porous medium problem characterised by Darcy’s law; whereas drug dynamics are characterised by a triple coupled advection-diffusion-reaction model. The microscopic properties of the malignant tissue are effectively encoded into a series of macroscopic coefficients, which enable the analysis of geometric changes at the microscale from a macroscopic perspective. We will briefly discuss analysis of the models’ isotropic case, which reveals the existence of an optimal permeability for lymphatic vessels, allowing for optimised fluid and drug transport. The purpose of this work is to create more general theoretical models, deepening our understanding of anti-cancer strategies.