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The vast majority of stars with mass similar to the Sun are expected to only destroy lithium over the course of their lives, via low-temperature nuclear burning. This has now been supported by observations of hundreds of thousands of red giant stars (Brown et al. 1989, Kumar et al. 2011, Deepak et al. 2019, Singh et al. 2019, Casey et al. 2019). Here we perform the first large-scale systematic investigation into the Li content of stars in the red clump phase of evolution, which directly follows the red giant branch phase. Surprisingly we find that all red clump stars have high levels of lithium for their evolutionary stage. On average the lithium content increases by a factor of 40 after the end of the red giant branch stage. This suggests that all low-mass stars undergo a lithium production phase between the tip of the red giant branch and the red clump. We demonstrate that our finding is not predicted by stellar theory, revealing a stark tension between observations and models. We also show that the heavily studied (Brown et al. 1989, Reddy et al. 2005, Kumar et al. 2011, Singh et al. 2019, Casey et al. 2019) very Li-rich giants, with A(Li) $> +1.5$ dex, represent only the extreme tail of the lithium enhancement distribution, comprising 3% of red clump stars. Our findings suggest a new definition limit for Li-richness in red clump stars, A(Li) $> -0.9$ dex, which is much lower than the limit of A(Li) $> +1.5$ dex used over many decades (Brown et al. 1989, Castilho et al. 1995, Reddy et al. 2005, Carlberg et al. 2016, Casey et al. 2019, Holanda et al. 2020).