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Despite the importance of thermal conductivity for a range of modern glass applications, its compositional dependence and structural origins in modified oxide glasses remain poorly understood. In particular, the thermal conductivity of oxide glasses with network formers other than silica remain almost unexplored and no thorough connection with structural characteristics of glasses has been made. In this work, we study the thermal conductivity of binary lithium borate glasses using both experiments and classical molecular dynamics (MD) simulations. This glass system is chosen due to the nonmonotonic evolution in the boron coordination number as a function of composition and because glasses may be made in a wide compositional window. Specifically, we show that thermal conductivity exhibits a clear boron anomaly effect, as observed in both experiments and MD simulations. Thermal conduction is thus believed to mainly be promoted by the presence of fourfold coordinated boron. However, simulated vibrational density of states for the studied series suggests that the thermal conductivity is also influenced by the presence of the modifier ions based on an observed overlap between Li and O modes. Overall these results provide insights into the connection between thermal conductivity and structure of modified oxide glasses, which is the first step toward developing a model for predicting the composition dependence of thermal conductivity.