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We report the serendipitous discovery of a very metal-poor (VMP) Li-richgiant star ($T_{\rm eff}$ = 4690$\pm$80 K, log g = 1.34$\pm$0.13, [Fe/H] =$-2.43\pm$0.07). We analyse the Li I 6103 and 6707 \r{A} lines accounting fordepartures from local thermodynamic equilibrium (NLTE) and correcting for 3Deffects using literature data, which yields a lithium abundance$\log\varepsilon_{Li} = 3.42\pm0.07$. Comparing lithium abundances from the twolines, in 1D NLTE we measure the isotope ratio $^6$Li/$^7$Li =1.64$^{+1.49}_{-1.08}$ %. When correcting for 3D effects, we detect the fragile$^6$Li isotope at $2$-sigma level and the ratio $^6$Li/$^7$Li =5.65$^{+5.05}_{-2.51}$ %. To our knowledge, this is the first $^6$Li/$^7$Limeasurement in an extremely Li-rich VMP star. The Cameron-Fowler mechanism,which is proposed to produce Li-rich stars, does not imply $^6$Li productionand is therefore inconsistent with our measurement when applying 3Dcorrections. We also derive NLTE abundances for 16 elements, most of which showsimilar abundances to those found in VMP stars. Sodium is an exception:[Na/Fe]$_{\rm NLTE, 1D}$ = 0.07 $\pm 0.03$, which is 0.5 dex higher than whatis typical for VMP stars. This star joins the sample of rare Li-rich VMP stars,and we offer a novel way to constrain the source of lithium in such starsthrough isotope ratio measurements.

The Pristine survey -- XXII. A serendipitous discovery of an extremely  Li-rich very metal-poor giant and a new method of $^6$Li/$^7$Li isotope  measurement