  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.
