Battery manufacturers aim to minimize greenhouse gas (GHG) emissions from producing lithium-ion battery (LIB) cells. Meeting these ambitions necessitates understanding how different factors throughout the value chain impact the GHG emissions from producing a LIB cell. In this article, we use a parametric process-based life cycle assessment (LCA) model to explore how the GHG emissions of lithium iron phosphate (LFP) and nickel manganese cobalt (NMC811) cells could potentially vary due to changes in the raw material supply parameters. The average global reference GHG emissions for producing 1 kWh functional unit of cell capacity is estimated in our model at 107 kgCO2e for LFP and 94 kgCO2e for NMC811. This paper further evaluates GHG emissions for cell manufacturing in Norway, Germany, and China, using global average conditions for raw material supply. In addition to the reference GHG estimates, thirty LCA scenarios are performed using a parameterization of raw material conditions. These scenarios involved changing ore grades, technology routes in mineral processing, material recovery efficiency, and the carbon intensity of the electricity mix for raw material processing. A global average mix, a Norwegian, German, and Chinese electricity mix are used for cell manufacturing. Based on specific ranges of raw material parameters, our estimation suggests that the theoretical emission ranges for LFP could be 27-64 kgCO2e/kWh for Norway, 60-98 kgCO2e/kWh for Germany, and 90-127 kgCO2e/kWh for China. For NMC811, the theoretical emissions range from 27 - 111 kgCO2e/kWh for Norway, 51-134 kgCO2e/kWh for Germany, and 71-155 kgCO2e/kWh for China. This work highlights the impact of raw supply chain conditions on the overall GHG emissions of Li-ion battery cells.