Integrated assessment models are generally not constrained by raw materials supply. In this article, the interactions between a wide diffusion of electric vehicles in the world transportation sector and the lithium supply are analysed in the Times Integrated Assessment Model (TIAM-IFPEN version). The lithium sector and a detailed representation of the transportation sector have been then implemented into the TIAM-IFPEN processes constituting the global energy system. Hence, the availability of this strategic material to supply the growing demand for low-carbon technologies in the context of the energy transition can be questioned. Incorporating an endogenous representation of the lithium supply chain allows investigating its dynamic criticality depending on several optimal technology paths that represent different climate and/or mobility scenarios between 2005 and 2050. It is the first detailed global bottom-up energy model with an endogenous disaggregated raw materials supply chain. Based on our simulations, the geological, geopolitical and economic dimensions of criticality are discussed. Four scenarios have been run: two climate scenarios (4 degrees C and 2 degrees C) with two shapes of mobility each: a high mobility where we consider the impact of urban dispersal with a huge car dependence/usage, and a low mobility in which the demand for individual road transport is lower due to a more sustainable urban planning and more public transport. The electric vehicles fleet should reach up to 1/3 of global fleet by 2050 in the 4 degrees C scenarios, while it could be up to 3/4 in the 2 degrees C scenarios both with high mobility, mostly located in Asian countries (China, India and other developing countries in Asia) due to the large presence of 2 and 3-wheelers. The penetration of electric vehicles has a major impact on lithium market. The cumulated demand over the period 2005-2050 reaches up to 53% of the current resources in the 2 degrees C scenario with a high mobility. These results tend to show an absence of geological criticality. Nevertheless, they have clearly highlighted other different forms of vulnerabilities, whether economic, industrial, geopolitical or environmental. A discussion about the future risk factors on the lithium market is done at a regional scale aiming at analysing more in-depth the impact of the electric vehicle on lithium market. Our study of this particular strategic material shows that the model could be a useful decision-making tool for assessing future raw material market in the context of the energy transition and could be extended to other critical raw materials for more efficient regional and sectorial screening.