LY Lup LSP and phase-folded Li positions (procedure as described in Campbell-White et al. (2021). The velocities are those measured from the reference wavelength of 6708 Å and are already corrected for stellar RV. The phase plots therefore represent the relative shift in Li position. Points are coloured by observations corresponding to different phases. The photometric period of 2.84d from Kiraga (2012) is one of the peaks from the periodogram. False-alarm probabilities are lower for the shorter periods (∼ 20%), but the significance is still low due to the number of data points.