Synthetic Lethality (SL) is currently defined as a type of genetic interaction in which the loss of function of either of two genes individually has limited effect in cell viability but inactivation of both genes simultaneously leads to cell death. Given the profound genomic aberrations acquired by tumor cells, which can be systematically identified with -omics data, SL is a promising concept in cancer research. In particular, SL has received much attention in the area of cancer metabolism, due to the fact that relevant functional alterations concentrate on key metabolic pathways that promote cellular proliferation. With the extensive prior knowledge about human metabolic networks, a number of computational methods have been developed to predict SL in cancer metabolism, including the genetic Minimal Cut Sets (gMCSs) approach. A major challenge in the application of SL approaches to cancer metabolism is to systematically integrate tumor microenvironment, given that genetic interactions and nutritional availability are interconnected to support proliferation. Here, we propose a more general definition of SL for cancer metabolism that combines genetic and environmental interactions, namely loss of gene functions and absence of nutrients in the environment. We extend our gMCSs approach to determine this new family of metabolic synthetic lethal interactions. A computational and experimental proof-of-concept is presented for predicting the lethality of dihydrofolate reductase (DHFR) inhibition in different environments. Finally, our approach is applied to identify extracellular nutrient dependences of tumor cells, elucidating cholesterol and myo-inositol depletion as potential vulnerabilities in different malignancies.