ABSTRACT Lithium’s susceptibility to burning in stellar interiors makes it an invaluable tracer for delineating the evolutionary pathways of stars, offering insights into the processes governing their development. Observationally, the complex Li production and depletion mechanisms in stars manifest themselves as Li plateaus, and as Li-enhanced and Li-depleted regions of the HR diagram. The Li-dip represents a narrow range in effective temperature close to the main-sequence turn-off, where stars have slightly super-solar masses and strongly depleted Li. To study the modification of Li through stellar evolution, we measure 3D non-local thermodynamic equilibrium (NLTE) Li abundance for 581 149 stars released in GALAH DR3. We describe a novel method that fits the observed spectra using a combination of 3D NLTE Li line profiles with blending metal-line strength that are optimized on a star-by-star basis. Furthermore, realistic errors are determined by a Monte Carlo nested sampling algorithm which samples the posterior distribution of the fitted spectral parameters. The method is validated by recovering parameters from a synthetic spectrum and comparing to 26 stars in the Hypatia catalogue. We find 228 613 Li detections, and 352 536 Li upper limits. Our abundance measurements are generally lower than GALAH DR3, with a mean difference of 0.23 dex. For the first time, we trace the evolution of Li-dip stars beyond the main sequence turn-off and up the subgiant branch. This is the first 3D NLTE analysis of Li applied to a large spectroscopic survey, and opens up a new era of precision analysis of abundances for large surveys.