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 [ 1 , 2 , 3 , 4 , 5 ] . 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 [ 1 , 6 , 2 , 4 , 5 ] 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 [ 1 , 7 , 6 , 8 , 5 , 9 ] .